Bounded weak solutions to nonlinear elliptic equations
A. El Hachimi, UFR Mathématiques Appliquées et Industrielles, El Jadida, Maroc E. J. Qualitative Theory of Diff. Equ., No. 10. (2009), pp. 1-16.
J. Igbida, UFR Mathématiques Appliquées et Industrielles, El Jadida, Maroc
| Communicated by J. B. Serrin. | Received on 2008-11-17 Appeared on 2009-03-12 |
Abstract: In this work, we are concerned with a class of elliptic problems with both absorption terms and critical growth in the gradient. We suppose that the data belong to $L^{m}(\Omega)$ with $m>n/2$ and we prove the existence of bounded weak solutions via $L^{\infty}$-estimates. A priori estimates and Stampacchia's $L^{\infty}$-regularity are our main ingredient.
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