Quasilinear elliptic problems with nonstandard growth

Abstract

We prove the existence of solutions to Dirichlet problems associated with the $p(x)$-quasilinear elliptic equation $$ Au =- hbox{div} a(x,u,abla u)= f(x,u,abla u). $$ These solutions are obtained in Sobolev spaces with variable exponents.

Keywords

• Quasilinear elliptic equation
• Sobolev spaces with variable exponent
• image processing
• Dirichlet problem