JournalszaaVol. 26 , No. 4DOI 10.4171/zaa/1335

On the Limiting Regularity Result of some Nonlinear Elliptic Equations

  • M. Kbiri Alaoui

    Ecole Mohammadia d'Ingénieurs, Rabat, Morocco
  • D. Meskine

    Ecole Supérieure de Technologie Essaouira, Morocco
  • A. Souissi

    Faculté des Sciences, Rabat, Morocco
On the Limiting Regularity Result of some Nonlinear Elliptic Equations cover

Abstract

We shall prove the limiting regularity W01,N(p1)N1(Ω)W_0^{1,\frac{N(p-1)}{N-1}}(\Omega ) of solutions of some nonlinear elliptic problems with right hand side in LLogαL(Ω)LLog^{\alpha}L(\Omega) and αN1N\alpha \geq \frac{N - 1}{N}. Also, an improved regularity is given when α<N1N\alpha < \frac{N - 1}{N}.