On the Limiting Regularity Result of some Nonlinear Elliptic Equations

Abstract

We shall prove the limiting regularity $W_0^{1,\frac{N(p-1)}{N-1}}(\Omega )$ of solutions of some nonlinear elliptic problems with right hand side in $LLo{g}^{\alpha }L(\Omega )$ and $\alpha \ge \frac{N-1}{N}$. Also, an improved regularity is given when $\alpha <\frac{N-1}{N}$.