A priori bounds and existence of solutions for some nonlocal elliptic problems

被引：20

作者：

Barrios, Begona ^{[1
]}

Del Pezzo, Leandro ^{[2
]}

Garcia-Melian, Jorge ^{[3
,4
]}

Quaas, Alexander ^{[5
]}

机构：

[1] Univ Texas Austin, Dept Math, RLM 8-100,2515 Speedway Stop,C1200, Austin, TX 78712 USA

[2] Consejo Nacl Invest Cient & Tecn, Dept Matemat, FCEyN UBA, Ciudad Univ Pab 1, RA-1428 Buenos Aires, DF, Argentina

[3] Univ La Laguna, Dept Anal Matemat, C Astrofis Francisco Sanche S-N, San Cristobal la Laguna 38271, Spain

[4] Univ La Laguna, Inst Univ Estudios Avanzados IUdEA Fis Atom Mol &, C Astrofis Francisco Sanche S-N, San Cristobal la Laguna 38203, Spain

[5] Univ Tecn Federico Santa Maria, Dept Matemat, Casilla V-110,Avda Espana, Valparaiso 1680, Chile

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2018年 / 34卷 / 01期

关键词：

Nonlocal diffusion problems; a priori estimates; topological degree; LIOUVILLE-TYPE THEOREMS; BREZIS-NIRENBERG RESULT; FRACTIONAL LAPLACIAN; DIRICHLET PROBLEM; EQUATIONS; REGULARITY; DIFFUSION; OPERATORS; POWER; DRIFT;

D O I：

10.4171/RMI/983

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we show existence of solutions for some elliptic problems with nonlocal diffusion by means of nonvariational tools. Our proof is based on the use of topological degree, which requires a priori bounds for the solutions. We obtain the a priori bounds by adapting the classical scaling method of Gidas and Spruck. We also deal with problems involving gradient terms.

引用

页码：195 / 220

页数：26

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