Renormalized solutions for p(x)-Laplacian equation with Neumann nonhomogeneous boundary condition

Renormalized solutions for a p(·)-Laplacian equation with Neumann nonhomogeneous boundary condition involving diffuse measure data and variable exponent

“…The existence of renormalized solutions for the problem (P µ ) where α is a real function and µ is L 1 or Radon measure data has been studied in [3,4]. Recently in [8], problem (P µ ) was studied with µ ∈ L 1 (Ω). In [3,4,8], under some assumptions the authors proved that the operator associated to the approximated problem is of type (M).…”

“…Recently in [8], problem (P µ ) was studied with µ ∈ L 1 (Ω). In [3,4,8], under some assumptions the authors proved that the operator associated to the approximated problem is of type (M). So, by some a priori estimates, they obtained the convergence of the approximate sequence to a renormalized solution of the initial problem.…”

“…So, by some a priori estimates, they obtained the convergence of the approximate sequence to a renormalized solution of the initial problem. In this work, we extend the approach developed in [3,4,8] to the case of maximal monotone graph or and Radon diffuse measure data. Elliptic problems with variable exponent has been extensively studied in recent years (see [3,4,5,6,7,9,18,19,20,22,23]) and the references therein.…”

“…In the case where S p(•) (E) = 0 we have Cap p(•) (E, Ω) = +∞. This work can be seen as a generalization of [8]. Our aim is to prove the existence of renormalized solutions to the general elliptic problem (P µ ).…”