Article ID Journal Published Year Pages File Type
4615470 Journal of Mathematical Analysis and Applications 2015 15 Pages PDF
Abstract

In this paper we prove existence, uniqueness, and regularity results for solutions of nonlinear elliptic equations in which the differential operator has logarithmic growth with respect to the gradient. The solution will belong to the Sobolev space W01,1(Ω), to the Orlicz–Sobolev space generated by the function tlog⁡(1+|t|)tlog⁡(1+|t|), but not to any Sobolev space W01,p(Ω), with p>1p>1.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
Authors
, ,