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Dissertations / Theses on the topic 'Nonlocal operators'

Author: Grafiati

Published: 9 March 2023

Last updated: 25 July 2025

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1

Dzhugan, Aleksandr <1994&gt. "Advanced properties of some nonlocal operators." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amsdottorato.unibo.it/10002/3/PhD%20Thesis%20Dzhugan.pdf.

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In this thesis, we deal with problems, related to nonlocal operators. In particular, we introduce a suitable notion of integral operators acting on functions with minimal requirements at infinity. We also present results of stability under the appropriate notion of convergence and compatibility results between polynomials of different orders. The theory is developed not only in the pointwise sense, but also in viscosity setting. Moreover, we discover the main properties of extremal type operators, with some applications. Then using the notion of viscosity solutions and Ishii-Lions technique,

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2

Schulze, Tim [Verfasser]. "Nonlocal operators with symmetric kernels / Tim Schulze." Bielefeld : Universitätsbibliothek Bielefeld, 2020. http://d-nb.info/1206592125/34.

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3

Bucur, C. D. "SOME NONLOCAL OPERATORS AND EFFECTS DUE TO NONLOCALITY." Doctoral thesis, Università degli Studi di Milano, 2017. http://hdl.handle.net/2434/488032.

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In this thesis, we deal with problems related to nonlocal operators, in particular to the fractional Laplacian and some other types of fractional derivatives. We make an extensive introduction to the fractional Laplacian and to some related contemporary research themes. We add to this some original material: the potential theory of this operator and a proof of Schauder estimates with the potential theory approach, the study of a fractional elliptic problem in $mathbb{R}^n$ with convex nonlinearities and critical growth, and a stickiness property of $s$-minimal surfaces as $s$ gets small. Also,

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4

BUCUR, CLAUDIA DALIA. "Some nonlocal operators and effects due to nonlocality." Doctoral thesis, Università degli Studi di Milano, 2017. http://hdl.handle.net/10281/277792.

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In this thesis, we deal with problems related to nonlocal operators, in particular to the fractional Laplacian and to some other types of fractional derivatives (the Caputo and the Marchaud derivatives). We make an extensive introduction to the fractional Laplacian, we present some related contemporary research results and we add some original material. Indeed, we study the potential theory of this operator, introduce a new proof of Schauder estimates using the potential theory approach, we study a fractional elliptic problem in Rn with convex nonlinearities and critical growth and we presen

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5

Voigt, Paul [Verfasser], and Moritz [Akademischer Betreuer] KaßMann. "Nonlocal operators on domains / Paul Voigt ; Betreuer: Moritz Kaßmann." Bielefeld : Universitätsbibliothek Bielefeld, 2017. http://d-nb.info/1139117726/34.

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6

Felsinger, Matthieu [Verfasser]. "Parabolic equations associated with symmetric nonlocal operators / Matthieu Felsinger." Bielefeld : Universitätsbibliothek Bielefeld, 2013. http://d-nb.info/1042557322/34.

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7

FRASSU, SILVIA. "Dirichlet problems for several nonlocal operators via variational and topological methods." Doctoral thesis, Università degli Studi di Cagliari, 2021. http://hdl.handle.net/11584/309589.

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The main topic of the thesis is the study of elliptic differential equations with fractional order driven by nonlocal operators, as the fractional p-Laplacian, the fractional Laplacian for p=2, the general nonlocal operator and its anisotropic version. Recently, great attention has been focused on the study of fractional and nonlocal operators of elliptic type, both for pure mathematical research and in view of concrete real-world applications. This type of operators arises in a quite natural way in many different contexts, such as, among others, game theory, image processing, optimization, ph

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8

Abatangelo, N. "Large Solutions for Fractional Laplacian Operators." Doctoral thesis, Università degli Studi di Milano, 2015. http://hdl.handle.net/2434/320258.

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The thesis studies linear and semilinear Dirichlet problems driven by different fractional Laplacians. The boundary data can be smooth functions or also Radon measures. The goal is to classify the solutions which have a singularity on the boundary of the prescribed domain. We first remark the existence of a large class of harmonic functions with a boundary blow-up and we characterize them in terms of a new notion of degenerate boundary trace. Via some integration by parts formula, we then provide a weak theory of Stampacchia's sort to extend the linear theory to a setting including these funct

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9

Foghem, Gounoue Guy Fabrice [Verfasser]. "$L^2$-Theory for nonlocal operators on domains / Guy Fabrice Foghem Gounoue." Bielefeld : Universitätsbibliothek Bielefeld, 2020. http://d-nb.info/1219215139/34.

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10

Chaker, Jamil [Verfasser], and Moritz [Akademischer Betreuer] KaßMann. "Analysis of anisotropic nonlocal operators and jump processes / Jamil Chaker ; Betreuer: Moritz Kaßmann." Bielefeld : Universitätsbibliothek Bielefeld, 2017. http://d-nb.info/1150181672/34.

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11

Ghilli, Daria. "Some Results in Nonlinear PDEs: Large Deviations Problems, Nonlocal Operators, and Stability for Some Isoperimetric Problems." Doctoral thesis, Università degli studi di Padova, 2016. http://hdl.handle.net/11577/3424479.

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This thesis is concerned with various problems arising in the study of nonlinear elliptic PDE. It is divided into three parts. In the first part we consider the short time behaviour of stochastic systems affected by a stochastic volatility evolving at a faster time scale. Our mathematical framework is that of multiple time scale systems and singular perturbations. We are concerned with the asymptotic behaviour of a logarithmic functional of the process, which we study by methods of the theory of homogenization and singular perturbations for fully nonlinear PDEs. We point out three regim

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12

Cao, Xinlin. "Geometric structures of eigenfunctions with applications to inverse scattering theory, and nonlocal inverse problems." HKBU Institutional Repository, 2020. https://repository.hkbu.edu.hk/etd_oa/754.

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Inverse problems are problems where causes for desired or an observed effect are to be determined. They lie at the heart of scientific inquiry and technological development, including radar/sonar, medical imaging, geophysical exploration, invisibility cloaking and remote sensing, to name just a few. In this thesis, we focus on the theoretical study and applications of some intriguing inverse problems. Precisely speaking, we are concerned with two typical kinds of problems in the field of wave scattering and nonlocal inverse problem, respectively. The first topic is on the geometric structures

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13

Pagliardini, Dayana. "Fractional minimal surfaces and Allen-Cahn equations." Doctoral thesis, Scuola Normale Superiore, 2018. http://hdl.handle.net/11384/85738.

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In recent years fractional operators have received considerable attention both in pure and applied mathematics. They appear in biological observations, finance, crystal dislocation, digital image reconstruction and minimal surfaces. In this thesis we study nonlocal minimal surfaces which are boundaries of sets minimizing certain integral norms and can be interpreted as a non-infinitesimal version of classical minimal surfaces. In particular, we consider critical points, with or withouth constraints, of suitable functionals, or approximations through diffuse models as the Allen-Cahn’s. In th

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14

Abatangelo, Nicola. "Large solutions for fractional Laplacian operators." Thesis, Amiens, 2015. http://www.theses.fr/2015AMIE0019/document.

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La thèse étudie les problèmes de Dirichlet linéaires et semilinéaires pour différents opérateurs du type Laplacien fractionnaire. Les données peuvent être des fonctions régularières [régulières] ou plus généralement des mesures de Radon. Le but est de classifier les solutions qui présentent une singularité au bord du domaine prescrit. Nous remarquons d'abord l'existence de toute une gamme de fonctions harmoniques explosant au bord et nous les caractérisons selon une nouvelle notion de trace au bord. A l'aide d'une nouvelle formule d'intégration par parties, nous élaborons ensuite une théorie f

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15

Almutairi, Fahad. "Nonlocal vector calculus." Kansas State University, 2018. http://hdl.handle.net/2097/38781.

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Master of Science<br>Department of Mathematics<br>Bacim Alali<br>Nonlocal vector calculus, introduced in generalizes differential operators' calculus to nonlocal calculus of integral operators. Nonlocal vector calculus has been applied to many fields including peridynamics, nonlocal diffusion, and image analysis. In this report, we present a vector calculus for nonlocal operators such as a nonlocal divergence, a nonlocal gradient, and a nonlocal Laplacian. In Chapter 1, we review the local (differential) divergence, gradient, and Laplacian operators. In addition, we discuss their adjoints, the

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16

Lopez, Rios Luis Fernando. "Two problems in nonlinear PDEs : existence in supercritical elliptic equations and symmetry for a hypo-elliptic operator." Thesis, Aix-Marseille, 2014. http://www.theses.fr/2014AIXM4701/document.

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Le travail présenté est dédié à des problèmes d'EDP non linéaires. L'idée principale est de construire des solutions régulières á certaines EDPs elliptiques et hypo-elliptiques et étudier leur propriétés qualitatives. Dans une première partie, on considère un problème sur-critique du type $$-Delta u = lambda e^u$$ avec $lambda > 0$ posé dans un domaine extérieur avec conditions de Dirichlet homogènes. Une réduction en dimension finie permet de prouver l'existence d'un nombre infini de solutions régulières quand $lambda$ est assez petit. Dans une deuxième partie, on étudie la concentration d

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17

Veruete, Mario. "Étude d'équations de réplication-mutation non locales en dynamique évolutive." Thesis, Montpellier, 2019. http://www.theses.fr/2019MONTS012/document.

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Nous analysons trois modèles non-locaux décrivant la dynamique évolutive d’un trait phénotypique continu soumis à l’action conjointe des mutations et de la sélection. Nous établissons l’existence et l’unicité des solutions du problème de Cauchy, et donnons la description du comportement en temps long de la solution. Dans le premier travail nous étudions l’équation du réplicateur-mutateur en domaine non borné et généralisons aux cas des valeurs sélectives confinantes les résultats connus dans le cas harmonique. À savoir, l’existence d’une unique solution globale, régulière, convergeant en temps

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18

Drungilaitė, Jolanta. "Diferencialinio uždavinio su nelokaliosiomis sąlygomis kompleksinių tikrinių reikšmių tyrimas." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2013. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2013~D_20130617_181725-06707.

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Šiame magistro baigiamajame darbe nagrinėjamas paprastasis diferencialinis operatorius su viena klasikine (pirmo arba antro tipo) sąlyga kairiajame intervalo krašte ir kita nelokaliąja (integraline, Samarskio ir Bitsadzės ar antro tipo) sąlyga dešiniajame intervalo gale. Mokslinėje literatūroje nemažai rašoma apie tokio uždavinio realiojo spektro struktūrą, tačiau kompleksinis spektras yra pakankamai mažai nagrinėjamas. Magistro baigiamajame darbe aprašyta šio uždavinio realiojo ir kompleksinio spektro struktūra, ištirtos kompleksinių tikrinių reikšmių teigiamųjų realiųjų dalių egzistavimo sąl

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19

Dilley, Daniel Jacob. "An Insight on Nonlocal Correlations in Two-Qubit Systems." OpenSIUC, 2016. https://opensiuc.lib.siu.edu/theses/2069.

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In this paper, we introduce the motivation for Bell inequalities and give some background on two different types: CHSH and Mermin's inequalities. We present a proof for each and then show that certain quantum states can violate both of these inequalities. We introduce a new result stating that for four given measurement directions of spin, two respectively from Alice and two from Bob, which are able to produce a violation of the Bell inequality for an arbitrary shared quantum state will also violate the Bell inequality for a maximally entangled state. Then we provide another new result that c

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20

Rapalytė, Svajūnė. "Diferencialinio uždavinio su kintamais koeficientais tyrimas." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2012. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2012~D_20120620_114424-38644.

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Magistro baigiamajame darbe nagrinėjamas diferencialinis operatorius su kintamais koeficientais ir viena klasikine, o kita nelokaliąja Samarskio ir Bitsadzės kraštine sąlyga. Šis uždavinys suvedamas į kanoninį pavidalą. Tiriamos kintamo koeficiento savybės, kaip jos keičiasi suvedant uždavinį į kanoninį pavidalą, taip pat tiriama šio uždavinio spektro priklausomybė nuo nelokaliosios kraštinės sąlygos parametrų.<br>In the Master's Thesis there is investigated a differential operator with variable coefficients, one classical and other nonlocal Samarskii-Bitsadze type boundary condition. There is

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21

Šiaulytė, Austėja. "Parabolinės lygties su nelokaliąja integraline Robino sąlyga išreikštinė skirtuminė schema." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2013. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2013~D_20130617_182830-33054.

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Magistro darbe yra tiriama parabolinės lygties su nelokaliąja integraline Robino sąlyga skirtuminė schema. Skirtuminės schemos stabilumui nagrinėti naudojama skirtuminio operatoriaus su nelokaliąja sąlyga spektro struktūros tyrimo metodika bei Maple programa, skirta kompiuteriniams eksperimentams atlikti. Atlikto magistro darbo rezultatai papildo iki šiol kitų mokslininkų gautus rezultatus tiriant parabolinių lygčių su nelokaliosiomis sąlygomis išreikštinių skirtuminių schemų tyrimus. Magistro darbą sudaro: įvadas, šešios pagrindinės dalys bei išvados. Įvadiniame skyriuje aptariamas temos aktu

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22

Ren, Huilong [Verfasser], Timon [Akademischer Betreuer] Rabczuk, Klaus [Gutachter] Guerlebeck, and Klaus [Gutachter] Hackl. "Dual-horizon peridynamics and Nonlocal operator method / Huilong Ren ; Gutachter: Klaus Guerlebeck, Klaus Hackl ; Betreuer: Timon Rabczuk." Weimar : Bauhaus-Universität Weimar, 2021. http://d-nb.info/1231715081/34.

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23

Savin, Anton Yu, та Boris Yu Sternin. "Index defects in the theory of nonlocal boundary value problems and the η-invariant". Universität Potsdam, 2001. http://opus.kobv.de/ubp/volltexte/2008/2614/.

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The paper deals with elliptic theory on manifolds with boundary represented as a covering space. We compute the index for a class of nonlocal boundary value problems. For a nontrivial covering, the index defect of the Atiyah-Patodi-Singer boundary value problem is computed. We obtain the Poincaré duality in the K-theory of the corresponding manifolds with singularities.

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24

Cozzi, M. "QUALITATIVE PROPERTIES OF SOLUTIONS OF NONLINEAR ANISOTROPIC PDES IN LOCAL AND NONLOCAL SETTINGS." Doctoral thesis, Università degli Studi di Milano, 2016. http://hdl.handle.net/2434/345873.

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La tesi è dedicata allo studio di varie proprietà qualitative possedute dalle soluzioni di equazioni ellittiche poste nello spazio euclideo. L'attenzione principale del lavoro è rivolta a soluzioni intere di equazioni anisotrope/eterogenee che mostrano qualche genere di proprietà di simmetria e, in particolare, che posseggono simmetria unidimensionale. L'elaborato è diviso in due parti. La prima parte è riservata ad equazioni alle derivate parziali locali, mentre la seconda si concentra su di una classe meno usuale di equazioni non locali, determinate da operatori integrali.<br>The thesis is

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25

Debroux, Noémie. "Mathematical modelling of image processing problems : theoretical studies and applications to joint registration and segmentation." Thesis, Normandie, 2018. http://www.theses.fr/2018NORMIR02/document.

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Dans cette thèse, nous nous proposons d'étudier et de traiter conjointement plusieurs problèmes phares en traitement d'images incluant le recalage d'images qui vise à apparier deux images via une transformation, la segmentation d'images dont le but est de délimiter les contours des objets présents au sein d'une image, et la décomposition d'images intimement liée au débruitage, partitionnant une image en une version plus régulière de celle-ci et sa partie complémentaire oscillante appelée texture, par des approches variationnelles locales et non locales. Les relations étroites existant entre ce

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26

MIRAGLIO, PIETRO. "ESTIMATES AND RIGIDITY FOR STABLE SOLUTIONS TO SOME NONLINEAR ELLIPTIC PROBLEMS." Doctoral thesis, Università degli Studi di Milano, 2020. http://hdl.handle.net/2434/704717.

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Questa tesi è incentrata sullo studio di equazioni differenziali alle derivate parziali di tipo ellittico. La prima parte della tesi riguarda la regolarità delle soluzioni stabili per un'equazione nonlineare con il p-Laplaciano, in un dominio limitato dello spazio Euclideo. La tecnica è basata sull'uso di disuguaglianze di tipo Hardy-Sobolev su ipersuperfici, del quale viene approfondito lo studio. Nella seconda parte viene preso in esame un problema nonlocale di tipo Dirichlet-Neumann. Studiamo la simmetria unidimensionale di alcune sottoclassi di soluzioni stabili, ottenendo risultati in dim

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27

CRUZ, Thamires Santos. "Uma teoria de regularidade para equações de volterra fracionárias com dados iniciais locais e não locais." Universidade Federal de Pernambuco, 2016. https://repositorio.ufpe.br/handle/123456789/18454.

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Submitted by Irene Nascimento (irene.kessia@ufpe.br) on 2017-03-29T19:13:09Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Tese-Thamires.pdf: 818214 bytes, checksum: 5697cce4e93e09e89c5150c064df333e (MD5)<br>Made available in DSpace on 2017-03-29T19:13:09Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Tese-Thamires.pdf: 818214 bytes, checksum: 5697cce4e93e09e89c5150c064df333e (MD5) Previous issue date: 2016-02-26<br>CNPQ<br>Este trabalho trata da teoria de existência, unicidade, reg

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Tapdigoglu, Ramiz. "Inverse problems for fractional order differential equations." Thesis, La Rochelle, 2019. http://www.theses.fr/2019LAROS004/document.

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Dans cette thèse, nous nous intéressons à résoudre certains problèmes inverses pour des équations différentielles aux dérivées fractionnaires. Un problème inverse est généralement mal posé. Un problème mal posé est un problème qui ne répond pas à l’un des trois critères de Hadamard pour être bien posé, c’est-à-dire, soit l’existence, l’unicité ou une dépendance continue aux données n'est plus vraie, à savoir, des petits changements dans les données de mesure entraînent des changements indéfiniment importants dans la solution. La plupart des difficultés à résoudre des problèmes mal posés sont c

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29

Nguyen, Thi Tuyen. "Comportement en temps long des solutions de quelques équations de Hamilton-Jacobi du premier et second ordre, locales et non-locales, dans des cas non-périodiques." Thesis, Rennes 1, 2016. http://www.theses.fr/2016REN1S089/document.

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La motivation principale de cette thèse est l'étude du comportement en temps grand des solutions non-bornées d'équations de Hamilton-Jacobi visqueuses dans RN en présence d'un terme d'Ornstein-Uhlenbeck. Nous considérons la même question dans le cas d'une équation de Hamilton-Jacobi du premier ordre. Dans le premier cas, qui constitue le cœur de la thèse, nous généralisons les résultats de Fujita, Ishii et Loreti (2006) dans plusieurs directions. La première est de considérer des opérateurs de diffusion plus généraux en remplaçant le Laplacien par une matrice de diffusion quelconque. Nous cons

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30

(6368468), Daesung Kim. "Stability for functional and geometric inequalities and a stochastic representation of fractional integrals and nonlocal operators." Thesis, 2019.

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<div>The dissertation consists of two research topics.</div><div><br></div><div>The first research direction is to study stability of functional and geometric inequalities. Stability problem is to estimate the deficit of a functional or geometric inequality in terms of the distance from the class of optimizers or a functional that identifies the optimizers. In particular, we investigate the logarithmic Sobolev inequality, the Beckner-Hirschman inequality (the entropic uncertainty principle), and isoperimetric type inequalities for the expected lifetime of Brownian motion. </div><div><br></div>

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