Non local diffusion equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:432

Article

Boegelein, Verena¹  Duzaar, Frank²  Marcellini, Paolo³  Signoriello, Stefano² 

[1] Salzburg Univ, Fachbereich Math, A-5020 Salzburg, Austria

[2] Univ Erlangen Nurnberg, Dept Math, D-91058 Erlangen, Germany

[3] Univ Florence, Dipartimento Matemat & Informat U Dini, I-50134 Florence, Italy

关键词: Existence of solutions;    Parabolic equations;    Variational minimizer;    Parabolic minimizer;    Non local partial differential equations;   

DOI  :  10.1016/j.jmaa.2015.06.053

来源: Elsevier

【 摘 要 】

In this paper we present a variational approach to establish the existence and uniqueness of variational solutions to nonlocal evolutionary problems. The model we have in mind is the following nonlocal version of the parabolic p-Laplacian u(t) - div [a(parallel to Du(t)parallel to L-p(p)(Omega)) vertical bar Du vertical bar(p-2) Du] = h, which has recently attracted many authors. We emphasize that our approach also applies in situations where the considered functionals do not allow the derivation of the associated Euler Lagrange equation. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free