On some nonlinear nonhomogeneous elliptic unilateral problems involving noncontrollable lower order terms with measure right hand side
Volume 40 / 2013
Applicationes Mathematicae 40 (2013), 197-219
MSC: Primary 47A15; Secondary 46A32, 47D20.
DOI: 10.4064/am40-2-4
Abstract
We prove the existence of entropy solutions to unilateral problems associated to equations of the type $Au-\mathop{\rm div}(\phi (u))=\mu \in L^{1}(\varOmega )+W^{-1,p'(\cdot )}(\varOmega )$, where $A$ is a Leray–Lions operator acting from $W_{0}^{1,p(\cdot )}(\varOmega )$ into its dual $W^{-1,p(\cdot )}(\varOmega )$ and $\phi \in C^{0}(\mathbb R,\mathbb R^{N})$.
