Mixed local and nonlocal elliptic operators: regularity and maximum principles

被引：105

作者：

Biagi, Stefano ^{[1
]}

Dipierro, Serena ^{[2
]}

Valdinoci, Enrico ^{[2
]}

Vecchi, Eugenio ^{[3
]}

机构：

[1] Politecn Milan, Dipartimento Matemat, Via Bonardi 9, I-20133 Milan, Italy

[2] Univ Western Australia, Dept Math & Stat, Crawley, WA, Australia

[3] Univ Bologna, Dipartimento Matemat, Bologna, Italy

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2022年 / 47卷 / 03期

基金：

澳大利亚研究理事会;

关键词：

Existence; maximum principle; operators of mixed order; qualitative properties of solutions; regularity; VISCOSITY SOLUTIONS; INTEGRODIFFERENTIAL EQUATIONS; THEOREM;

D O I：

10.1080/03605302.2021.1998908

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We develop a systematic study of the superpositions of elliptic operators with different orders, mixing classical and fractional scenarios. For concreteness, we focus on the sum of the Laplacian and the fractional Laplacian, and we provide structural results, including existence, maximum principles (both for weak and classical solutions), interior Sobolev regularity and boundary regularity of Lipschitz type.

引用

页码：585 / 629

页数：45

共 49 条

[1]

Abatangelo N., 2019, SPRINGER INDAM SER, V33, P1

[2] AN ELLIPTIC BOUNDARY VALUE PROBLEM WITH FRACTIONAL NONLINEARITY [J].

Abatangelo, Nicola ;

Cozzi, Matteo .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2021, 53 (03) :3577-3601

[3] The Liouville theorem and linear operators satisfying the maximum principle [J].

Alibaud, Nathael ;

del Teso, Felix ;

Endal, Jorgen ;

Jakobsen, Espen R. .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2020, 142 :229-242

[4] Second-order elliptic integro-differential equations: viscosity solutions' theory revisited [J].

Barles, B. ;

Imbert, Cyril .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2008, 25 (03) :567-585

[5] Large time behavior of periodic viscosity solutions for uniformly parabolic integro-differential equations [J].

Barles, Guy ;

Chasseigne, Emmanuel ;

Ciomaga, Adina ;

Imbert, Cyril .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2014, 50 (1-2) :283-304

[6] Lipschitz regularity of solutions for mixed integro-differential equations [J].

Barles, Guy ;

Chasseigne, Emmanuel ;

Ciomaga, Adina ;

Imbert, Cyril .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (11) :6012-6060

[7] A Widder's Type Theorem for the Heat Equation with Nonlocal Diffusion [J].

Barrios, Begona ;

Peral, Ireneo ;

Soria, Fernando ;

Valdinoci, Enrico .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2014, 213 (02) :629-650

[8] Holder continuity of harmonic functions with respect to operators of variable order [J].

Bass, RF ;

Kassmann, M .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2005, 30 (08) :1249-1259

[9] Harnack inequalities for non-local operators of variable order [J].

Bass, RF ;

Kassmann, M .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 357 (02) :837-850

[10] Semilinear elliptic equations involving mixed local and nonlocal operators [J].

Biagi, Stefano ;

Vecchi, Eugenio ;

Dipierro, Serena ;

Valdinoci, Enrico .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2021, 151 (05) :1611-1641

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