Multivalued problem with Robin boundary condition involving diffuse measure data and variable exponent

Abstract

We study a nonlinear elliptic problem with Robin type boundary condition, governed by a general Leray–Lions operator with variable exponents and diffuse Radon measure data which does not charge the sets of zero p(·)-capacity. We prove an existence and uniqueness result of a weak solution.

Keywords

• robin boundary condition
• diffuse measure
• biting lemma of chacon
• maximal monotone graph
• radon measure data
• weak solution
• entropic solution
• leray–lions operator
• subdifferential operator
• 35k55
• 35d05