Open AccessUniqueness for elliptic problems with Hölder--type dependence on the solution
Author(s) -
Lucio Boccardo,
Alessio Porretta
Publication year - 2012
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2013.12.1569
Subject(s) - uniqueness , nabla symbol , bounded function , mathematics , dirichlet problem , weak solution , type (biology) , omega , mathematical analysis , dirichlet distribution , pure mathematics , boundary value problem , elliptic curve , physics , ecology , quantum mechanics , biology
We prove uniqueness of weak (or entropy) solutions for nonmonotone elliptic equations of the type -div(a (x, u)del u) = f in a bounded set Omega subset of R-N with Dirichlet boundary conditions. The novelty of our results consists in the possibility to deal with cases when a (x, u) is only Holder continuous with respect to u