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

Abstract:
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.

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