Polyharmonic k-Hessian equations in RN

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:265

Article

Balodis, Pedro¹  Escudero, Carlos¹ 

[1] Univ Autonoma Madrid, Dept Matemat, Madrid, Spain

关键词: Higher order elliptic equations;    k-Hessian type equations;    Existence of solutions;    Fixed point methods;    Functional inequalities;    Harmonic analysis of partial differential equations;   

DOI  :  10.1016/j.jde.2018.04.057

来源: Elsevier

【 摘 要 】

This work is focused on the study of the nonlinear elliptic higher order equation (-Delta)(m) u = S-k[-u] + lambda f, x is an element of R-N, where the k-Hessian S-k[u] is the kth elementary symmetric polynomial of eigenvalues of the Hessian matrix of the solution and the datum f belongs to a suitable functional space. This problem is posed in R-N and we prove the existence of at least one solution by means of topological fixed point methods for suitable values of m is an element of N. Questions related to the regularity of the solutions and extensions of these results to the nonlocal setting are also addressed. On the way to construct these proofs, some technical results such as a fixed point theorem and a refinement of the critical Sobolev embedding, which could be of independent interest, are introduced. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free