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Academic literature on the topic 'Moser-Trudinger'

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Published: 14 March 2023

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Journal articles on the topic "Moser-Trudinger"

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Song, Xiaoping, Dongliang Li, and Maochun Zhu. "Critical and Subcritical Anisotropic Trudinger–Moser Inequalities on the Entire Euclidean Spaces." Mathematical Problems in Engineering 2021 (September 30, 2021): 1–13. http://dx.doi.org/10.1155/2021/8992411.

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We investigate the subcritical anisotropic Trudinger–Moser inequality in the entire space ℝ N , obtain the asymptotic behavior of the supremum for the subcritical anisotropic Trudinger–Moser inequalities on the entire Euclidean spaces, and provide a precise relationship between the supremums for the critical and subcritical anisotropic Trudinger–Moser inequalities. Furthermore, we can prove critical anisotropic Trudinger–Moser inequalities under the nonhomogenous norm restriction and obtain a similar relationship with the supremums of subcritical anisotropic Trudinger–Moser inequalities.
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Kim, Meelae. "Linearised Moser-Trudinger inequality." Bulletin of the Australian Mathematical Society 62, no. 3 (December 2000): 445–57. http://dx.doi.org/10.1017/s0004972700018967.

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As a limiting case of the Sobolev imbedding theorem, the Moser-Trudinger inequality was obtained for functions in with resulting exponential class integrability. Here we prove this inequality again and at the same time get sharper information for the bound. We also generalise the Linearised Moser inequality to higher dimensions, which was first introduced by Beckner for functions on the unit disc. Both of our results are obtained by using the method of Carleson and Chang. The last section introduces an analogue of each inequality for the Laplacian instead of the gradient under some restricted conditions.
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Cianchi, Andrea. "Moser–Trudinger trace inequalities." Advances in Mathematics 217, no. 5 (March 2008): 2005–44. http://dx.doi.org/10.1016/j.aim.2007.09.007.

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MANCINI, G., and K. SANDEEP. "MOSER–TRUDINGER INEQUALITY ON CONFORMAL DISCS." Communications in Contemporary Mathematics 12, no. 06 (December 2010): 1055–68. http://dx.doi.org/10.1142/s0219199710004111.

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We prove that a sharp Moser–Trudinger inequality holds true on a conformal disc if and only if the metric is bounded from above by the Poincaré metric. We also derive necessary and sufficient conditions for the validity of a sharp Moser–Trudinger inequality on a simply connected domain in ℝ2.
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Hyder, Ali. "Moser functions and fractional Moser–Trudinger type inequalities." Nonlinear Analysis 146 (November 2016): 185–210. http://dx.doi.org/10.1016/j.na.2016.08.024.

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Wang, Guofang, and Dong Ye. "A Hardy–Moser–Trudinger inequality." Advances in Mathematics 230, no. 1 (May 2012): 294–320. http://dx.doi.org/10.1016/j.aim.2011.12.001.

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del Pino, Manuel, Monica Musso, and Bernhard Ruf. "Beyond the Trudinger-Moser supremum." Calculus of Variations and Partial Differential Equations 44, no. 3-4 (August 25, 2011): 543–76. http://dx.doi.org/10.1007/s00526-011-0444-5.

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Dolbeault, Jean, Maria J. Esteban, and Gaspard Jankowiak. "The Moser-Trudinger-Onofri inequality." Chinese Annals of Mathematics, Series B 36, no. 5 (August 7, 2015): 777–802. http://dx.doi.org/10.1007/s11401-015-0976-7.

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Santaria Leuyacc, Yony Raúl. "Nonlinear Elliptic Equations with Maximal Growth Range." Pesquimat 20, no. 1 (September 4, 2017): 1. http://dx.doi.org/10.15381/pes.v20i1.13753.

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En este trabajo nos interesa estudiar la existencia de soluciones débiles no triviales para una clase de ecuaciones elípticas no lineales definidas en un dominio limitado en dimensión dos, donde las no linealidades poseen un rango de crecimiento exponencial máximo motivado por las desigualdades de Trudinger-Moser en espacios de Lorentz-Sobolev. Para estudiar la solubilidad se utiliza un enfoque variacional. Más específicamente, usamos el teorema del paso de montaña junto con desigualdades de tipo Trudinger-Moser.
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Li, Jungang, Guozhen Lu, and Maochun Zhu. "Concentration-Compactness Principle for Trudinger–Moser’s Inequalities on Riemannian Manifolds and Heisenberg Groups: A Completely Symmetrization-Free Argument." Advanced Nonlinear Studies 21, no. 4 (October 10, 2021): 917–37. http://dx.doi.org/10.1515/ans-2021-2147.

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Abstract The concentration-compactness principle for the Trudinger–Moser-type inequality in the Euclidean space was established crucially relying on the Pólya–Szegő inequality which allows to adapt the symmetrization argument. As far as we know, the first concentration-compactness principle of Trudinger–Moser type in non-Euclidean settings, such as the Heisenberg (and more general stratified) groups where the Pólya–Szegő inequality fails, was found in [J. Li, G. Lu and M. Zhu, Concentration-compactness principle for Trudinger–Moser inequalities on Heisenberg groups and existence of ground state solutions, Calc. Var. Partial Differential Equations 57 2018, 3, Paper No. 84] by developing a nonsmooth truncation argument. In this paper, we establish the concentration-compactness principle of Trudinger–Moser type on any compact Riemannian manifolds as well as on the entire complete noncompact Riemannian manifolds with Ricci curvature lower bound. Our method is a symmetrization-free argument on Riemannian manifolds where the Pólya–Szegő inequality fails. This method also allows us to give a completely symmetrization-free argument on the entire Heisenberg (or stratified) groups which refines and improves a proof in the paper of Li, Lu and Zhu. Our results also show that the bounds for the suprema in the concentration-compactness principle on compact manifolds are continuous and monotone increasing with respect to the volume of the manifold.
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Dissertations / Theses on the topic "Moser-Trudinger"

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BEZERRA, Flank David Morais. "Desigualdades do tipo Trudinger-Moser e aplicações." Universidade Federal de Campina Grande, 2006. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1150.

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Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-07-11T20:27:42Z No. of bitstreams: 1 FLANK DAVID MORAIS BEZERRA - DISSERTAÇÃO PPGMAT 2006..pdf: 680785 bytes, checksum: 70ecc5db691a5b5a00bbc5eada32bb1b (MD5)
Made available in DSpace on 2018-07-11T20:27:42Z (GMT). No. of bitstreams: 1 FLANK DAVID MORAIS BEZERRA - DISSERTAÇÃO PPGMAT 2006..pdf: 680785 bytes, checksum: 70ecc5db691a5b5a00bbc5eada32bb1b (MD5) Previous issue date: 2006-12
Capes
Neste trabalho estimamos algumas das desigualdades do tipo Trudinger-Moser, a fim de estudar as propriedades dos funcionais energia associados à problemas elípticos não-lineares onde a não-linearidade possui crescimento crítico. A fortiri, utilizando técnicas variacionais estudamos existência e multiplicidade de solução para tais problemas.
In this work we appreciate some Trudinger-Moser type inequality for to study the behaviour of the functional energy the semilinear Dirichlet problems with critical growth. Later, apply variational methods we study existence and multiplicity of solution for such problems.
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Zghal, Mohamed Khalil. "Inégalités de type Trudinger-Moser et applications." Thesis, Paris Est, 2016. http://www.theses.fr/2016PESC1077/document.

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Cette thèse porte sur quelques inégalités de type Trudinger-Moser et leurs applications à l'étude des injections de Sobolev qu'elles induisent dans les espaces d'Orlicz et à l'analyse d'équations aux dérivées partielles non linéaires à croissance exponentielle.Le travail qu'on présente ici se compose de trois parties. La première partie est consacrée à la description du défaut de compacité de l'injection de Sobolev 4D dans l'espace d'Orlicz dansle cadre radial.L'objectif de la deuxième partie est double. D'abord, on caractérise le défaut de compacité de l'injection de Sobolev 2D dans les différentes classes d'espaces d'Orlicz. Ensuite, on étudiel'équation de Klein-Gordon semi-linéaire avec non linéarité exponentielle, où la norme d'Orlicz joue un rôle crucial. En particulier, on aborde les questions d'existence globale, de complétude asymptotique et d'étude qualitative.Dans la troisième partie, on établit des inégalités optimales de type Adams, en étroite relation avec les inégalités de Hardy, puis on fournit une description du défaut de compacité des injections de Sobolev qu'elles induisent
This thesis focuses on some Trudinger-Moser type inequalities and their applications to the study of Sobolev embeddings they induce into the Orlicz spaces, and the investigation of nonlinear partial differential equations with exponential growth.The work presented here includes three parts. The first part is devoted to the description of the lack of compactness of the 4D Sobolev embedding into the Orlicz space in the radialframework.The aim of the second part is twofold. Firstly, we characterize the lack of compactness of the 2D Sobolev embedding into the different classes of Orlicz spaces. Secondly, we undertakethe study of the nonlinear Klein-Gordon equation with exponential growth, where the Orlicz norm plays a crucial role. In particular, issues of global existence, scattering and qualitativestudy are investigated.In the third part, we establish sharp Adams-type inequalities invoking Hardy inequalities, then we give a description of the lack of compactness of the Sobolev embeddings they induce
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Santos, Izabela Andrade dos. "Métodos variacionais, desigualdade do tipo Trudinger-Moser e aplicações." Universidade Federal de Sergipe, 2017. https://ri.ufs.br/handle/riufs/5815.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this work, we are interested in establishing some variational methods, together with applications, that determine the existence and non uniqueness of weak solutions for the nonlinear elliptic partial differential equation −div (K(x)-u) = K(x)f(u) + h, x E R2, where K is an exponential weight, h is a linear functional and f is the nonlinearity that presents critical exponential growth. First of all, for the sake of convenience of the reader, this study shows detailed proofs of some classic results of the theory that involves these methods as, for example, the deformation and mountain pass theorems; and Ekeland’s variational principle. Second of all, we work with a Trudinger-Moser inequality that is related to a Sobolev space with weight K in order to achieve our aim.
Neste trabalho, estamos interessados em apresentar alguns Métodos Variacionais, juntamente com aplicações, que determinam existência e a não unicidade de soluções fracas para uma específica Equação Diferencial Parcial Elíptica não linear −div (K(x)-u) = K(x)f(u) + h, x E R2, onde K é um peso exponencial, h é um funcional linear e f é a não linearidade que apresenta crescimento exponencial crítico. Em um primeiro momento, para uma maior comodidade do leitor, estabelecemos provas detalhadas de alguns resultados clássicos da teoria que contém esses métodos como, por exemplo, os Teoremas da Deformação e do Passo da Montanha; e o Princípio Variacional de Ekeland. Em seguida, trabalhamos com uma Desigualdade do tipo Trudinger-Moser em um Espaço de Sobolev com peso K com o objetivo de alcançarmos nossa meta.
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Mancini, Gabriele. "Sharp Inequalities and Blow-up Analysis for Singular Moser-Trudinger Embeddings." Doctoral thesis, SISSA, 2015. http://hdl.handle.net/20.500.11767/4861.

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We investigate existence of solutions for a singular Liouville equation on S^2 and prove sharp Onofri-type inequalities for a Moser-Trudinger functional in the presence of singular potentials. As a consequence we obtain existence of extremal functions for the Moser-Trudinger embedding on compact surfaces with conical singularities. Finally we study the blow-up behavior for sequences of solutions Liouville-type systems and prove a compactness condition which plays an important role in the variational analysis of Toda systems.
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Felix, Diego Dias. "Sobre uma classe de problemas elípticos envolvendo o crescimento do tipo Trudinger-Moser." Universidade Federal da Paraíba, 2015. http://tede.biblioteca.ufpb.br:8080/handle/tede/9263.

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Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq
In this work, we study a class of quasilinear elliptic problem involving nonlinearities with subcritical polynomial growth, subcritical exponential growth and critical exponential growth. Our main focus is to treat nonlinearities which do not satisfy the condition of super-quadratic of Ambrosetti-Rabinowitz. Our main tool is the Mountain Pass Theorem with the Cerami condition.
Neste trabalho, estudamos uma classe de problemas elípticos quase lineares envolvendo não linearidades com crescimento polinomial subcrítico, exponencial subcrítico e exponencial crítico. Nosso foco principal é tratar não linearidades que não satisfazem a condição de superquadraticidade de Ambrosetti-Rabinowitz. A nossa ferramenta é o Teorema do Passo da Montanha com a condição de Cerami.
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Albuquerque, Francisco Sibério Bezerra. "Uma desigualdade do tipo Trudinger-Moser em espaços de Sobolev com peso e aplicações." Universidade Federal da Paraí­ba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/7428.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
This work addresses a class of Trudinger-Moser type inequalities in weighted Sobolev spaces in R2. As an application of these inequalities and by using variational methods, we establish sufficient conditions for the existence, multiplicity and nonexistence of solutions for some classes of nonlinear Schrödinger elliptic equations (and systems of equations) with unbounded, singular or decaying radial potentials and involving nonlinearities with exponential critical growth of Trudinger-Moser type.
Este trabalho aborda uma classe de desigualdades do tipo Trudinger-Moser em espaços de Sobolev com peso em R2. Como aplicação destas desigualdades e usando métodos variacionais, estabeleceremos condições suficientes para a existência, multiplicidade e não-existência de soluções para algumas classes de equações (e sistemas de equações) de Schrödinger elípticas não-lineares com potenciais radiais ilimitados, singulares na origem ou decaindo a zero no infinito e envolvendo não-linearidades com crescimento crítico exponencial do tipo Trudinger-Moser.
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Leuyacc, Yony Raúl Santaria. "Equações parciais elípticas com crescimento exponencial." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-17032014-103611/.

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Neste trabalho estudamos existência, multiplicidade e não existência de soluções não triviais para o seguinte problema elíptico: { - \'DELTA\' = f(x, u), em \'OMEGA\' u = 0, sobre \'\\PARTIAL\' \'OMEGA\', onde \'OMEGA\' é um conjunto limitado de \'R POT. 2\' com fronteira suave e a função f possui crescimento exponencial. Para a existência de soluções são aplicados métodos variacionais combinados com as desigualdades de Trudinger-Moser. O resultado de não-existência é restrito ao caso de soluções radiais positivas e \'OMEGA\' = \'B IND.1\'(0). A prova usa técnicas de equações diferenciais ordinárias
In this work we study the existence, multiplicity and non-existence of non-trivial solutions to the following elliptic problem: { - \'DELTA\' u = f(x; u); in \'OMEGA\', ; u = 0; on \'\\PARTIAL\' \'OMEGA\' where \"OMEGA\' is a bounded and smooth domain in \'R POT. 2\' and f possesses exponential growth. The existence results are proved by using variational methods and the Trudinger- Moser inequalities. The non-existence result is restricted to the case of positive radial solutions and \'OMEGA\' = \'B IND. 1\'(0). The proof uses techniques of the theory of ordinary differential equations.
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Araújo, Gustavo da Silva. "Sobre Soluções de Equações Elípticas Envolvendo o N-Laplaciano e Crescimento Crítico Exponencial." Universidade Federal da Paraí­ba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/7407.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
In this work, we study existence, multiplicity and nonexistence of positive solutions, with respect to a positive parameter , for a class of quasilinear elliptic problems in bounded domains of RN, N 2, involving the N-laplacian operator and a nonlinearity f(t) which behaves as t, for some 2 (0;N1), when t ! 0+ and has critical exponential growth of Trudinger-Moser type at +1. In order to obtain the results, we have used minimax theorems, sub and supersolution methods and a refinement of the Trudinger- Moser inequality due to P.-L. Lions.
Neste trabalho, estudamos existência, multiplicidade e não-existência de soluções positivas, com respeito a um parâmetro positivo , para uma classe de problemas elípticos quasilineares em domínios limitados de RN, N 2, envolvendo o operador N-laplaciano e uma não-linearidade f(t) que se comporta como tá, para algum 2 (0;N 1), quando t ! 0+ e possui crescimento crítico exponencial do tipo Trudinger-Moser em +1. Na obtenção dos resultados, podemos destacar a utilização de teoremas do tipo minimax, métodos de sub e supersolução e um refinamento da Desigualdade de Trudinger-Moser devido a P.-L. Lions.
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Battaglia, Luca. "Variational aspects of singular Liouville systems." Doctoral thesis, SISSA, 2015. http://hdl.handle.net/20.500.11767/4857.

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I studied singular Liouville systems on compact surfaces from a variational point of view. I gave sufficient and necessary conditions for the existence of globally minimizing solutions, then I found min-max solutions for some particular systems. Finally, I also gave some non-existence results.
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Leuyacc, Yony Raúl Santaria. "On Hamiltonian elliptic systems with exponential growth in dimension two." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-02082017-150001/.

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In this work we study the existence of nontrivial weak solutions for some Hamiltonian elliptic systems in dimension two, involving a potential function and nonlinearities which possess maximal growth with respect to a critical curve (hyperbola). We consider four different cases. First, we study Hamiltonian systems in bounded domains with potential function identically zero. The second case deals with systems of equations on the whole space, the potential function is bounded from below for some positive constant and satisfies some integrability conditions, while the nonlinearities involve weight functions containing a singulatity at the origin. In the third case, we consider systems with coercivity potential functions and nonlinearities with weight functions which may have singularity at the origin or decay at infinity. In the last case, we study Hamiltonian systems, where the potential can be unbounded or can vanish at infinity. To establish the existence of solutions, we use variational methods combined with Trudinger-Moser type inequalities for Lorentz-Sobolev spaces and a finite-dimensional approximation.
Neste trabalho estudamos a existência de soluções fracas não triviais para sistemas hamiltonianos do tipo elíptico, em dimensão dois, envolvendo uma função potencial e não linearidades tendo crescimento exponencial máximo com respeito a uma curva (hipérbole) crítica. Consideramos quatro casos diferentes. Primeiramente estudamos sistemas de equações em domínios limitados com potencial nulo. No segundo caso, consideramos sistemas de equações em domínio ilimitado, sendo a função potencial limitada inferiormente por alguma constante positiva e satisfazendo algumas de integrabilidade, enquanto as não linearidades contêm funções-peso tendo uma singularidade na origem. A classe seguinte envolve potenciais coercivos e não linearidades com funções peso que podem ter singularidade na origem ou decaimento no infinito. O quarto caso é dedicado ao estudo de sistemas em que o potencial pode ser ilimitado ou decair a zero no infinito. Para estabelecer a existência de soluções, utilizamos métodos variacionais combinados com desigualdades do tipo Trudinger-Moser em espaços de Lorentz-Sobolev e a técnica de aproximação em dimensão finita.
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Book chapters on the topic "Moser-Trudinger"

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Ghoussoub, Nassif, and Amir Moradifam. "Trudinger-Moser-Onofri inequality on 𝕊²." In Mathematical Surveys and Monographs, 263–73. Providence, Rhode Island: American Mathematical Society, 2013. http://dx.doi.org/10.1090/surv/187/18.

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Calanchi, Marta. "Some Weighted Inequalities of Trudinger–Moser Type." In Analysis and Topology in Nonlinear Differential Equations, 163–74. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-04214-5_9.

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Lam, Nguyen, and Guozhen Lu. "Sharp Singular Trudinger-Moser-Adams Type Inequalities with Exact Growth." In Geometric Methods in PDE’s, 43–80. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-02666-4_3.

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Chang, Sun-Yung. "The Moser-Trudinger inequality and applications to some problems in conformal geometry." In IAS/Park City Mathematics Series, 65–125. Providence, Rhode Island: American Mathematical Society, 1995. http://dx.doi.org/10.1090/pcms/002/03.

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Ruzhansky, Michael, and Nurgissa Yessirkegenov. "New Progress on Weighted Trudinger–Moser and Gagliardo–Nirenberg, and Critical Hardy Inequalities on Stratified Groups." In Landscapes of Time-Frequency Analysis, 277–89. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-05210-2_11.

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"Trudinger-Moser Inequality." In Free Energy and Self-Interacting Particles, 59–77. Boston, MA: Birkhäuser Boston, 2005. http://dx.doi.org/10.1007/0-8176-4436-9_4.

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Ding, Wei-Yue, and Gang Tian. "The Generalized Moser-Trudinger Inequality." In Peking University Series in Mathematics, 253–66. World Scientific, 2017. http://dx.doi.org/10.1142/9789813220881_0022.

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Sandeep, Kunnath. "Moser-Trudinger and Adams Inequalities." In Computational Science and Its Applications, 135–48. Chapman and Hall/CRC, 2020. http://dx.doi.org/10.1201/9780429288739-9.

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"Is the Trudinger-Moser nonlinearity a true critical nonlinearity?" In Conference Publications 2011. AIMS Press, 2011. http://dx.doi.org/10.3934/proc.2011.2011.1378.

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Ishiwata, Michinori. "ON THE EXISTENCE AND NONEXISTENCE OF MAXIMIZERS ASSOCIATED WITH TRUDINGER-MOSER TYPE INEQUALITIES IN UNBOUNDED DOMAINS." In Emerging Topics on Differential Equations and Their Applications, 41–53. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814449755_0004.

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Conference papers on the topic "Moser-Trudinger"

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Berezhnoi, Eugenii I., Victoria V. Kocherova, and Alexei A. Perfilyev. "Notes for Trudinger–Moser inequality." In INTERNATIONAL CONFERENCE “FUNCTIONAL ANALYSIS IN INTERDISCIPLINARY APPLICATIONS” (FAIA2017). Author(s), 2017. http://dx.doi.org/10.1063/1.5000608.

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