On a Class of Quasilinear Elliptic Equations with Degenerate Coerciveness and Measure Data

Abstract

We study the existence of measure-valued solutions for a class of degenerate elliptic equations with measure data. The notion of solution is natural, since it is obtained by a regularization procedure which also relies on a standard approximation of the datum μ. We provide partial uniqueness results and qualitative properties of the constructed solutions concerning, in particular, the structure of their diffuse part with respect to the harmonic-capacity.

Keywords

• measure-valued solutions
• degenerate elliptic equations
• radon measures
• 35j15
• 35d30
• 28a33