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1. A sparse optimization approach to infinite infimal convolution regularization NSTL国家科技图书文献中心

Bredies, Kristian | Carioni, Marcello ... - 《Numerische Mathematik》 - 2025,157(1) - 41～96 - 共56页

摘要：In this paper we introduce the class of | infinite infimal convolution functionals and apply these | functionals to the regularization of ill-posed inverse | problems. The proposed regularization involves an infimal | convolution of a continuously parametrized family of convex

关键词： 65J20 | 65K10 | 49J45 | 35R11

2. Multi-peak solutions for a fractional elliptic problem with slightly subcritical growth NSTL国家科技图书文献中心

Deng, Shengbing | Yu, Fang - 《Manuscripta mathematica》 - 2025,176(1) - 共40页

摘要：In this paper, by finite dimensional Lyapunov | -Schmidt reduction methods, we prove the existence of | concentrating solutions for a nonlocal problem involving the | slightly subcritical non-power type nonlinearity on a | bounded domain, under the assumption that a function

关键词： 35R11 | 35B33

3. Initial-Value Problem for Distributed-Order Equations with a Bounded Operator NSTL国家科技图书文献中心

V. E. Fedorov | A. A. Abdrakhmanova - 《Journal of mathematical sciences》 - 2025,287(6) - 826～834 - 共9页

摘要：Abstract Using methods of the theory of the | Laplace transform, we prove a theorem on the existence | of a unique solution to an initial-value problem | for a distributed-order differential equation in a | Banach space, which involves a fractional

关键词： 34K30 | 35R11 | 34G10

4. Continuity of s -minimal functions NSTL国家科技图书文献中心

Bucur, Claudia | Dipierro, Serena ... - 《Calculus of variations and partial differential equations》 - 2025,64(2) - 共17页

摘要：We consider the minimization property of a | Gagliardo-Slobodeckij seminorm which can be seen as the | fractional counterpart of the classical problem of | functions of least gradient and which is related to the | minimization of the nonlocal perimeter functional. We discuss

关键词： 35R11 | 58E12 | 35J60

5. A Grid-Overlay Finite Difference Method for Inhomogeneous Dirichlet Problems of the Fractional Laplacian on Arbitrary Bounded Domains NSTL国家科技图书文献中心

Weizhang Huang | Jinye Shen - 《Journal of scientific computing》 - 2025,102(2) - 1.1～1.26 - 共26页

摘要：Abstract A grid-overlay finite difference | method (GoFD) was proposed recently for the numerical | solution of homogeneous Dirichlet boundary value problems | of the fractional Laplacian on arbitrary bounded | domains and shown to have advantages of both finite

关键词： 65N06 | 35R11

6. On the Boltzmann equation with strong kinetic singularity and its grazing limit from a new perspective NSTL国家科技图书文献中心

Yang, Tong | Zhou, Yu-Long - 《Mathematische Annalen》 - 2025,391(4) - 4911～4995 - 共85页

摘要：For the inverse power law potential U(r) = r | (-p), the Boltzmann kernel has theasymptotic | behavior B (v - v(& lowast;), sigma)similar to theta(-2 | v-v(& lowast;)|(gamma )as the deviation angle | tends to 0. Global well-posedness of the Boltzmann

关键词： 35Q20 | 35R11

7. A fractional approach to strain-gradient plasticity: beyond core-radius of discrete dislocations NSTL国家科技图书文献中心

Almi, Stefano | Caponi, Maicol ... - 《Mathematische Annalen》 - 2025,391(3) - 4063～4115 - 共53页

摘要：We derive a strain-gradient theory for | plasticity as the Gammadocumentclass[12pt]{minimal | } usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts | } usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs | } usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin

关键词： 26A33 | 35R11 | 49J45 | 74C05

8. Gradient flow solutions for porous medium equations with nonlocal Lévy-type pressure NSTL国家科技图书文献中心

Foghem, Guy | Padilla-Garza, David ... - 《Calculus of variations and partial differential equations》 - 2025,64(3) - 共50页

摘要：We study a porous medium-type equation whose | pressure is given by a nonlocal L & eacute;vy operator | associated to a symmetric jump L & eacute;vy kernel. The | class of nonlocal operators under consideration | appears as a generalization of the classical fractional

关键词： 35A15 | 35R09 | 35R11 | 46E35 | 47A07 | 49J40 | 35S10

9. Local multiplicity for fractional linear equations with Hardy potentials NSTL国家科技图书文献中心

Mainini, Edoardo | Ognibene, Roberto ... - 《Calculus of variations and partial differential equations》 - 2025,64(2) - 共20页

摘要：We exhibit existence of non-trivial solutions | of some fractional linear Schr & ouml;dinger | equations which are radial and vanish at the origin. This | is in stark contrast to what happens in the local | case. We also prove analogous results in the presence

关键词： 35A02 | 35R11 | 35B40 | 35J75

10. C 1,α regularity of hypersurfaces of bounded nonlocal mean curvature in Riemannian manifolds NSTL国家科技图书文献中心

Moy, Julien - 《Calculus of variations and partial differential equations》 - 2025,64(1) - 共36页

摘要：Let (M, g) be a smooth connected Riemannian | manifold. We show an improvement of flatness theorem for | hypersurfaces of M of bounded nonlocal mean curvature in the | viscosity sense. It implies local C-1,C-alpha regularity | of these hypersurfaces provided that they are

摘要：In this paper we introduce the class of | infinite infimal convolution functionals and apply these | functionals to the regularization of ill-posed inverse | problems. The proposed regularization involves an infimal | convolution of a continuously parametrized family of convex

关键词： 65J20 | 65K10 | 49J45 | 35R11

摘要：In this paper, by finite dimensional Lyapunov | -Schmidt reduction methods, we prove the existence of | concentrating solutions for a nonlocal problem involving the | slightly subcritical non-power type nonlinearity on a | bounded domain, under the assumption that a function

关键词： 35R11 | 35B33

摘要：Abstract Using methods of the theory of the | Laplace transform, we prove a theorem on the existence | of a unique solution to an initial-value problem | for a distributed-order differential equation in a | Banach space, which involves a fractional

关键词： 34K30 | 35R11 | 34G10

摘要：We consider the minimization property of a | Gagliardo-Slobodeckij seminorm which can be seen as the | fractional counterpart of the classical problem of | functions of least gradient and which is related to the | minimization of the nonlocal perimeter functional. We discuss

关键词： 35R11 | 58E12 | 35J60

摘要：Abstract A grid-overlay finite difference | method (GoFD) was proposed recently for the numerical | solution of homogeneous Dirichlet boundary value problems | of the fractional Laplacian on arbitrary bounded | domains and shown to have advantages of both finite

关键词： 65N06 | 35R11

摘要：For the inverse power law potential U(r) = r | (-p), the Boltzmann kernel has theasymptotic | behavior B (v - v(& lowast;), sigma)similar to theta(-2 | v-v(& lowast;)|(gamma )as the deviation angle | tends to 0. Global well-posedness of the Boltzmann

关键词： 35Q20 | 35R11

摘要：We derive a strain-gradient theory for | plasticity as the Gammadocumentclass[12pt]{minimal | } usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts | } usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs | } usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin

关键词： 26A33 | 35R11 | 49J45 | 74C05

摘要：We study a porous medium-type equation whose | pressure is given by a nonlocal L & eacute;vy operator | associated to a symmetric jump L & eacute;vy kernel. The | class of nonlocal operators under consideration | appears as a generalization of the classical fractional

关键词： 35A15 | 35R09 | 35R11 | 46E35 | 47A07 | 49J40 | 35S10

摘要：We exhibit existence of non-trivial solutions | of some fractional linear Schr & ouml;dinger | equations which are radial and vanish at the origin. This | is in stark contrast to what happens in the local | case. We also prove analogous results in the presence

关键词： 35A02 | 35R11 | 35B40 | 35J75

摘要：Let (M, g) be a smooth connected Riemannian | manifold. We show an improvement of flatness theorem for | hypersurfaces of M of bounded nonlocal mean curvature in the | viscosity sense. It implies local C-1,C-alpha regularity | of these hypersurfaces provided that they are

关键词： 49Q05 | 35R11 | 58J35 | 45H99

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