Relevant bibliographies by topics / Sobolev spaces

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Sobolev spaces'

Author: Grafiati
Published: 4 June 2021
Last updated: 30 July 2024

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Journal articles on the topic "Sobolev spaces"

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Ichinose, Takashi, and Yoshimi Saito. "Dirac–Sobolev Spaces and Sobolev Spaces." Funkcialaj Ekvacioj 53, no. 2 (2010): 291–310. http://dx.doi.org/10.1619/fesi.53.291.

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Pustylnik, Evgeniy. "Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz-Sobolev embeddings." Journal of Function Spaces and Applications 3, no. 2 (2005): 183–208. http://dx.doi.org/10.1155/2005/254184.

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LetDkfmean the vector composed by all partial derivatives of orderkof a functionf(x),x∈Ω⊂ℝn. Given a Banach function spaceA, we look for a possibly small spaceBsuch that‖f‖B≤c‖|Dkf|‖Afor allf∈C0k(Ω). The estimates obtained are applied to ultrasymmetric spacesA=Lφ,E,B=Lψ,E, giving some optimal (or rather sharp) relations between parameter-functionsφ(t)andψ(t)and new results for embeddings of Orlicz-Sobolev spaces.
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Evans, W. D. "SOBOLEV SPACES." Bulletin of the London Mathematical Society 19, no. 1 (January 1987): 95–96. http://dx.doi.org/10.1112/blms/19.1.95.

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Johnson, Raymond. "Sobolev spaces." Acta Applicandae Mathematicae 8, no. 2 (February 1987): 199–205. http://dx.doi.org/10.1007/bf00046713.

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OHNO, TAKAO, and TETSU SHIMOMURA. "SOBOLEV INEQUALITIES FOR RIESZ POTENTIALS OF FUNCTIONS IN OVER NONDOUBLING MEASURE SPACES." Bulletin of the Australian Mathematical Society 93, no. 1 (November 12, 2015): 128–36. http://dx.doi.org/10.1017/s0004972715001331.

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Chen, Shutao, Changying Hu, and Charles Xuejin Zhao. "Extreme points and rotundity of Orlicz-Sobolev spaces." International Journal of Mathematics and Mathematical Sciences 32, no. 5 (2002): 293–99. http://dx.doi.org/10.1155/s0161171202202252.

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It is well known that Sobolev spaces have played essential roles in solving nonlinear partial differential equations. Orlicz-Sobolev spaces are generalized from Sobolev spaces. In this paper, we present sufficient and necessary conditions of extreme points of Orlicz-Sobolev spaces. A sufficient and necessary condition of rotundity of Orlicz-Sobolev spaces is obtained.
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Yang, Dachun, and Yong Lin. "SPACES OF LIPSCHITZ TYPE ON METRIC SPACES AND THEIR APPLICATIONS." Proceedings of the Edinburgh Mathematical Society 47, no. 3 (October 2004): 709–52. http://dx.doi.org/10.1017/s0013091503000907.

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AbstractNew spaces of Lipschitz type on metric-measure spaces are introduced and they are shown to be just the well-known Besov spaces or Triebel–Lizorkin spaces when the smooth index is less than 1. These theorems also hold in the setting of spaces of homogeneous type, which include Euclidean spaces, Riemannian manifolds and some self-similar fractals. Moreover, the relationships amongst these Lipschitz-type spaces, Hajłasz–Sobolev spaces, Korevaar–Schoen–Sobolev spaces, Newtonian Sobolev space and Cheeger–Sobolev spaces on metric-measure spaces are clarified, showing that they are the same space with equivalence of norms. Furthermore, a Sobolev embedding theorem, namely that the Lipschitz-type spaces with large orders of smoothness can be embedded in Lipschitz spaces, is proved. For metric-measure spaces with heat kernels, a Hardy–Littlewood–Sobolev theorem is establish, and hence it is proved that Lipschitz-type spaces with small orders of smoothness can be embedded in Lebesgue spaces.AMS 2000 Mathematics subject classification: Primary 42B35. Secondary 46E35; 58J35; 43A99
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Gröger, Konrad, and Lutz Recke. "Preduals of Sobolev-Campanato spaces." Mathematica Bohemica 126, no. 2 (2001): 403–10. http://dx.doi.org/10.21136/mb.2001.134016.

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Gaczkowski, Michał, and Przemysław Górka. "Variable Hajłasz-Sobolev spaces on compact metric spaces." Mathematica Slovaca 67, no. 1 (February 1, 2017): 199–208. http://dx.doi.org/10.1515/ms-2016-0258.

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Abstract We study variable exponent Sobolev spaces on compact metric spaces. Without the assumption of log-Hölder continuity of the exponent, the compact Sobolev-type embeddings theorems for these spaces are shown.
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Evans, W. D. "WEIGHTED SOBOLEV SPACES." Bulletin of the London Mathematical Society 18, no. 2 (March 1986): 220–21. http://dx.doi.org/10.1112/blms/18.2.220.

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Dissertations / Theses on the topic "Sobolev spaces"

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Clemens, Jason. "Sobolev spaces." Kansas State University, 2014. http://hdl.handle.net/2097/18186.

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Master of Science
Department of Mathematics
Marianne Korten
The goal for this paper is to present material from Gilbarg and Trudinger’s Elliptic Partial Differential Equations of Second Order chapter 7 on Sobolev spaces, in a manner easily accessible to a beginning graduate student. The properties of weak derivatives and there relationship to conventional concepts from calculus are the main focus, that is when do weak and strong derivatives coincide. To enable the progression into the primary focus, the process of mollification is presented and is widely used in estimations. Imbedding theorems and compactness results are briefly covered in the final sections. Finally, we add some exercises at the end to illustrate the use of the ideas presented throughout the paper.
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Gjestland, Fredrik Joachim. "Distributions, Schwartz Space and Fractional Sobolev Spaces." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2013. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-23452.

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This thesis derives the theory of distributions, starting with test functions as a basis. Distributions and their derivatives will be analysed and exemplified. Schwartz functions are introduced, and the Fourier transform of Schwartz functions is analysed, creating the basis for Tempered distributions on which we also analyse the Fourier transform. Weak derivatives and Sobolev spaces are defined, and from the Fourier transform we define Sobolev spaces of non-integer order. The theory presented is applied to an initial value problem with a derivative of order one in time and an arbitrary differentiation operator in space, and we take a look at conditions for well-posedness under different differnetiation operators and present some minor results. The Riesz representation theorem and the Lax--Milgram theorem are presented in order to offer a different perspective on the results from the initial value problem.
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Kydyrmina, Nurgul. "Operators in Sobolev Morrey spaces." Doctoral thesis, Università degli studi di Padova, 2013. http://hdl.handle.net/11577/3423455.

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Morrey spaces were introduced by Charles Morrey in 1938. They are a useful tool in the regularity theory of partial differential equations, in real analysis and in mathematical physics. In the nineties of the XX century an active study of general Morrey-type spaces characterized by a functional parameter has started to develop. A number of results on boundedness of classical operators in general Morrey-type spaces were obtained. At the beginning of the XXI century there were new active developments in this area. In the last decade many mathematicians do research on smoothness spaces related to Morrey spaces. Among these spaces the Sobolev-type spaces play an important role. In the thesis Sobolev spaces built on Morrey spaces are studied, which are also referred to as Sobolev Morrey spaces. These are spaces of functions which have derivatives up to certain order in Morrey spaces. We analyze some basic properties of Morrey spaces and of Sobolev Morrey spaces. Then we consider the embedding and multiplication operators in Sobolev Morrey spaces. Finally, the dissertation provides a study of the composition operator in Sobolev Morrey spaces. The results presented in the thesis have been obtained under supervision of Professors V.I. Burenkov and M. Lanza de Cristoforis.
Gli spazi di Morrey sono stati introdotti da Charles Morrey nel 1938. Essi sono uno strumento utile nella teoria della regolarità per equazioni differenziali alle derivate parziali, in analisi reale ed in fisica matematica. Negli anni novanta del XX secolo ha iniziato a svilupparsi un attivo studio degli spazi di Morrey di tipo generalizzato che sono caratterizzati da un parametro funzionale. E' stato ottenuto un cero numero di risultati sulla limitatezza degli operatori classici negli spazi di Morrey di tipo generalizzato. All'inizio del XXI secolo ci sono stati nuovi e attivi sviluppi in questa area. Nell'ultima decade molti matematici hanno svolto ricerche su spazi funzionali relativi agli spazi di Morrey. Tra questi spazi gli spazi di tipo Sobolev giocano un ruolo importante. Nella tesi si studiano Spazi di Sobolev costruiti su spazi di Morrey, anche detti spazi di Sobolev Morrey. Questi sono spazi di funzioni che hanno derivate fino ad un certo ordine negli spazi di Morrey. Si analizzano alcune proprietà di base degli spazi di Morrey e degli spazi di Sobolev-Morrey. Poi si considerano operatori di immersione e di moltiplicazione negli spazi di Sobolev Morrey. La terza parte della tesi presenta uno studio degli operatori di composizione negli spazi di Sobolev Morrey. I risultati presentati nella tesi sono stati ottenuti sotto la supervisione dei Professori V.I. Burenkov and M. Lanza de Cristoforis.
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Färm, David. "Upper gradients and Sobolev spaces on metric spaces." Thesis, Linköping University, Department of Mathematics, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-5816.

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The Laplace equation and the related p-Laplace equation are closely associated with Sobolev spaces. During the last 15 years people have been exploring the possibility of solving partial differential equations in general metric spaces by generalizing the concept of Sobolev spaces. One such generalization is the Newtonian space where one uses upper gradients to compensate for the lack of a derivative.

All papers on this topic are written for an audience of fellow researchers and people with graduate level mathematical skills. In this thesis we give an introduction to the Newtonian spaces accessible also for senior undergraduate students with only basic knowledge of functional analysis. We also give an introduction to the tools needed to deal with the Newtonian spaces. This includes measure theory and curves in general metric spaces.

Many of the properties of ordinary Sobolev spaces also apply in the generalized setting of the Newtonian spaces. This thesis includes proofs of the fact that the Newtonian spaces are Banach spaces and that under mild additional assumptions Lipschitz functions are dense there. To make them more accessible, the proofs have been extended with comments and details previously omitted. Examples are given to illustrate new concepts.

This thesis also includes my own result on the capacity associated with Newtonian spaces. This is the theorem that if a set has p-capacity zero, then the capacity of that set is zero for all smaller values of p.

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Park, Young Ja. "Sobolev trace inequality and logarithmic Sobolev trace inequality." Digital version:, 2000. http://wwwlib.umi.com/cr/utexas/fullcit?p9992883.

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Spector, Daniel. "Characterization of Sobolev and BV Spaces." Research Showcase @ CMU, 2011. http://repository.cmu.edu/dissertations/78.

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This work presents some new characterizations of Sobolev spaces and the space of functions of Bounded Variation. Additionally it gives new proofs of continuity and lower semicontinuity theorems due to Reshetnyak.
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Neves, Julio Severino. "Fractional Sobolev-type spaces and embeddings." Thesis, University of Sussex, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341514.

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Dines, Nicoleta, Gohar Harutjunjan, and Bert-Wolfgang Schulze. "The Zaremba problem in edge Sobolev spaces." Universität Potsdam, 2003. http://opus.kobv.de/ubp/volltexte/2008/2661/.

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Mixed elliptic boundary value problems are characterised by conditions which have a jump along an interface of codimension 1 on the boundary. We study such problems in weighted edge Sobolev spaces and show the Fredholm property and the existence of parametrices under additional conditions of trace and potential type on the interface. Our methods from the calculus of boundary value problems on a manifold with edges will be illustrated by the Zaremba problem and other mixed problems for the Laplace operator.
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Davidsson, Johan. "Sobolev Spaces and the Finite Element Method." Thesis, Örebro universitet, Institutionen för naturvetenskap och teknik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:oru:diva-67470.

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In this essay we present the Sobolev spaces and some basic properties of them. The Sobolev spaces serve as a theoretical framework for studying solutions to partial differential equations. The finite element method is presented which is a numerical method for solving partial differential equations.
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Clavero, Nadia F. "Optimal Sobolev Embeddings in Spaces with Mixed Norm." Doctoral thesis, Universitat de Barcelona, 2015. http://hdl.handle.net/10803/292613.

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Este proyecto hace referencia a estimaciones, en espacios funcionales, que relacionan la norma de una función y la de sus derivadas. Concretamente, nuestro principal objetivo es estudiar las estimaciones clásicas de las inclusiones de Sobolev, probadas por Gagliardo y Nirenberg, para derivadas de orden superior y espacios más generales. En particular, estamos interesados en describir el dominio y el rango óptimos para estas inclusiones entre los espacios invariantes por reordenamiento (r.i.) y espacios de normas mixtas.
This thesis project concerns estimates, in function spaces, that relate the norm of a function and that of its derivatives. Speci.cally, our main purpose is to study the classical Sobolev-type inequalities due to Gagliardo and Nirenberg for higher order derivatives and more general spaces. In particular, we concentrate on seeking the optimal domains and the optimal ranges for these embeddings between rearrangement-invariant spaces (r.i.) and mixed norm spaces.
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Books on the topic "Sobolev spaces"

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Maz'ya, Vladimir. Sobolev Spaces. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-15564-2.

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Maz’ja, Vladimir G. Sobolev Spaces. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-662-09922-3.

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Kufner, Alois. Weighted Sobolev spaces. Chichester: Wiley, 1985.

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Mazʹi︠a︡, V. G. Sobolev spaces in mathematics. New York: Springer, 2009.

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Burenkov, Victor I. Sobolev Spaces on Domains. Wiesbaden: Vieweg+Teubner Verlag, 1998. http://dx.doi.org/10.1007/978-3-663-11374-4.

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Burenkov, Victor I. Sobolev spaces on domains. Stuttgart: B.G. Teubner, 1998.

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G, Mazʹi︠a︡ V., and Isakov Victor 1947-, eds. Sobolev spaces in mathematics. New York: Springer, 2009.

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G, Mazʹi︠a︡ V., and Isakov Victor 1947-, eds. Sobolev spaces in mathematics. New York: Springer, 2009.

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Hebey, Emmanuel. Sobolev Spaces on Riemannian Manifolds. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/bfb0092907.

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Maz’ya, Vladimir, ed. Sobolev Spaces In Mathematics I. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-85648-3.

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Book chapters on the topic "Sobolev spaces"

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Maz’ja, Vladimir G. "Imbedding of the Space into Other Function Spaces." In Sobolev Spaces, 424–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-662-09922-3_12.

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Kress, Rainer. "Sobolev Spaces." In Linear Integral Equations, 125–51. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-0559-3_8.

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Willem, Michel. "Sobolev Spaces." In Cornerstones, 111–37. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7004-5_6.

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Krantz, Steven G., and Harold R. Parks. "Sobolev Spaces." In The Geometry of Domains in Space, 143–55. Boston, MA: Birkhäuser Boston, 1999. http://dx.doi.org/10.1007/978-1-4612-1574-5_4.

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Duistermaat, J. J., and J. A. C. Kolk. "Sobolev Spaces." In Distributions, 311–20. Boston: Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4675-2_19.

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Motreanu, Dumitru, Viorica Venera Motreanu, and Nikolaos Papageorgiou. "Sobolev Spaces." In Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems, 1–13. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-9323-5_1.

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Kress, Rainer. "Sobolev Spaces." In Linear Integral Equations, 141–70. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-9593-2_8.

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Harjulehto, Petteri, and Peter Hästö. "Sobolev Spaces." In Lecture Notes in Mathematics, 123–44. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-15100-3_6.

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Brenner, Susanne C., and L. Ridgway Scott. "Sobolev Spaces." In Texts in Applied Mathematics, 23–47. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4757-3658-8_2.

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Aubin, Thierry. "Sobolev Spaces." In Some Nonlinear Problems in Riemannian Geometry, 32–69. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-13006-3_2.

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Conference papers on the topic "Sobolev spaces"

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Pick, Luboš. "Optimality of function spaces in Sobolev embeddings." In V International Course of Mathematical Analysis in Andalusia. WORLD SCIENTIFIC, 2016. http://dx.doi.org/10.1142/9789814699693_0003.

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Fetzer, Matthias, and Carsten W. Scherer. "Stability and performance analysis on Sobolev spaces." In 2016 IEEE 55th Conference on Decision and Control (CDC). IEEE, 2016. http://dx.doi.org/10.1109/cdc.2016.7799390.

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He, Wenjie, and Mingjun Lai. "Bivariate box spline wavelets in Sobolev spaces." In SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, edited by Andrew F. Laine, Michael A. Unser, and Akram Aldroubi. SPIE, 1998. http://dx.doi.org/10.1117/12.328149.

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Baust, Maximilian, Darko Zikic, and Nassir Navab. "Variational Level Set Segmentation in Riemannian Sobolev Spaces." In British Machine Vision Conference 2014. British Machine Vision Association, 2014. http://dx.doi.org/10.5244/c.28.39.

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DEMIDENKO, GENNADII V. "WEIGHTED SOBOLEV SPACES AND QUASIELLIPTIC OPERATORS IN RN." In Proceedings of the 3rd ISAAC Congress. World Scientific Publishing Company, 2003. http://dx.doi.org/10.1142/9789812794253_0051.

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YAKUBOVICH, SEMYON B. "SOBOLEV TYPE SPACES ASSOCIATED WITH THE KONTOROVICH-LEBEDEV TRANSFORM." In Proceedings of the 5th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812835635_0021.

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Epperlein, Jonathan P., and Bassam Bamieh. "Distributed control of spatially invariant systems over Sobolev spaces." In 2014 European Control Conference (ECC). IEEE, 2014. http://dx.doi.org/10.1109/ecc.2014.6862545.

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Kushpel, A., and S. Tozoni. "Entropy Numbers of Sobolev and Besov Classes on Homogeneous Spaces." In Proceedings of the 4th International ISAAC Congress. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701732_0006.

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Koller, Michael, Johannes Grobmann, Ullrich Monich, and Holger Boche. "Deformation Stability of Deep Convolutional Neural Networks on Sobolev Spaces." In ICASSP 2018 - 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2018. http://dx.doi.org/10.1109/icassp.2018.8462158.

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Aydın, İsmail. "On Some Properties of Lorentz-Sobolev Spaces with Variable Exponent." In 4th International Symposium on Innovative Approaches in Engineering and Natural Sciences. SETSCI, 2019. http://dx.doi.org/10.36287/setsci.4.6.009.

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