Comparison results for nonlinear divergence structure elliptic PDE’s-Reference-Cited by-同舟云学术

Comparison results for nonlinear divergence structure elliptic PDE’s

Published:2019-06-01 Issue:1 Volume:9 Page:438-448
ISSN:2191-950X
Container-title:Advances in Nonlinear Analysis
language:en
Short-container-title:

Author:

Liu Yichen¹,Marras Monica²,Porru Giovanni²

Affiliation:

1. Department of Mathematical Sciences , Xi’an Jiaotong-Liverpool University , Suzhou , China

2. Department of Mathematics and Informatics , University of Cagliari , Cagliari , Italy

Abstract

Abstract First we prove a comparison result for a nonlinear divergence structure elliptic partial differential equation. Next we find an estimate of the solution of a boundary value problem in a domain Ω in terms of the solution of a related symmetric boundary value problem in a ball B having the same measure as Ω. For p-Laplace equations, the corresponding result is due to Giorgio Talenti. In a special (radial) case we also prove a reverse comparison result.

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Reference11 articles.

1. G. Talenti, Elliptic equations and rearrangements, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 3, (1976), no. 4, 697–718.

2. G. Talenti, The art of rearranging, Milan J. Math. 84, (2016), no. 1, 105–157.

3. B. Emamizadeh, Y. Liu and G. Porru, Extensions of a result by G. Talenti to (p, q)-Laplace equations, Nonlinear Anal. 180, (2019), 41–51.

4. P. Candito, S.A. Marano and K. Perera, On a class of critical (p, q)-Laplacian problems, NoDEA Nonlinear Differential Equations Appl. 22, (2015), no. 6, 1959–1972.

5. S. A. Marano and N. S. Papageorgiou, Constant-sign and nodal solutions of coercive (p, q)-Laplacian problems, Nonlinear Anal. 77, (2013), 118–129.

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