Electron. J. Diff. Eqns., Vol. 2002(2002), No. 54, pp. 1-8.

Nonexistence of solutions for quasilinear elliptic equations with p-growth in the gradient

Darko Zubrinic

We study the nonexistence of weak solutions in $W^{1,p}_{{\rm loc}}(\Omega)$ for a class of quasilinear elliptic boundary-value problems with natural growth in the gradient. Nonsolvability conditions involve general domains with possible singularities of the right-hand side. In particular, we show that if the data on the right-hand side are sufficiently large, or if inner radius of $\Omega$ is large, then there are no weak solutions.

Submitted April 17, 2002. Published June 11, 2002.
Math Subject Classifications: 35J25, 35J60, 45J05.
Key Words: Quasilinear elliptic, existence, nonexistence, geometry of domains.

Show me the PDF file (256K), TEX file, and other files for this article.

Darko Zubrinic
Faculty of Electrical Engineering and Computing,
Department of Applied Mathematics,
Unska 3, 10000 Zagreb, Croatia
e-mail: darko.zubrinic@fer.hr
Return to the EJDE web page