Geometric inequalities for fractional Laplace operators and applications

被引：5

作者：

Cinti, Eleonora ^{[1
]}

Ferrari, Fausto ^{[2
]}

机构：

[1] Wierstrass Inst Appl Anal & Stochast, D-10117 Berlin, Germany

[2] Univ Bologna, Dipartimento Matemat, I-40126 Bologna, Italy

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2015年 / 22卷 / 06期

关键词：

Weighted Poincare inequalities of fractional order; Fractional Laplacian; Hardy-type inequalities;

D O I：

10.1007/s00030-015-0340-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a weighted fractional inequality involving the solution u of a nonlocal semilinear problem in . Such inequality bounds a weighted L (2)-norm of a compactly supported function I center dot by a weighted H (s) -norm of I center dot. In this inequality a geometric quantity related to the level sets of u will appear. As a consequence we derive some relations between the stability of u and the validity of fractional Hardy inequalities.

引用

页码：1699 / 1714

页数：16

共 25 条

[1] A NOTION OF NONLOCAL CURVATURE [J].

Abatangelo, Nicola ;

Valdinoci, Enrico .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2014, 35 (7-9) :793-815

[2]

[Anonymous], 1990, Hardy-Type Inequalities, Pitman Research Notes in Mathematics Series 219

[3]

[Anonymous], 2001, T MAT I STEKLOVA

[4] Layer solutions in a half-space for boundary reactions [J].

Cabré, X ;

Solà-Morales, J .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2005, 58 (12) :1678-1732

[5] Sharp energy estimates for nonlinear fractional diffusion equations [J].

Cabre, Xavier ;

Cinti, Eleonora .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2014, 49 (1-2) :233-269

[6] ENERGY ESTIMATES AND 1-D SYMMETRY FOR NONLINEAR EQUATIONS INVOLVING THE HALF-LAPLACIAN [J].

Cabre, Xavier ;

Cinti, Eleonora .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2010, 28 (03) :1179-1206

[7] An extension problem related to the fractional Laplacian [J].

Caffarelli, Luis ;

Silvestre, Luis .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (7-9) :1245-1260

[8]

D'Ambrosio L, 2005, ANN SCUOLA NORM-SCI, V4, P451

[9]

Davila J., ARXIV14024173

[10] Local behavior of fractional p-minimizers [J].

Di Castro, Agnese ;

Kuusi, Tuomo ;

Palatucci, Giampiero .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2016, 33 (05) :1279-1299

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