Opuscula Math. 29, no. 4 (2009), 377-391
On elliptic problems with a nonlinearity depending on the gradient
Jan Chabrowski
Abstract.
We investigate the solvability of the Neumann problem \((1.1)\) involving the nonlinearity depending on the gradient. We prove the existence of a solution when the right hand side \(f\) of the equation belongs to \(L^m(\Omega )\) with \(1 \leq m \lt 2\).
Keywords:
Neumann problem, nonlinearity depending on the gradient, \(L^1\) data.
Mathematics Subject Classification:
35D05, 35J25, 35J60.
About the authors ▼
Jan Chabrowski
University of Queensland, Department of Mathematics, St. Lucia 4072, Qld, Australia
About the article ▼
Received: 2009-07-29.
Accepted: 2009-08-17.
Cite this article as ▼
Jan Chabrowski, On elliptic problems with a nonlinearity depending on the gradient, Opuscula Math. 29, no. 4 (2009), 377-391,
http://dx.doi.org/10.7494/OpMath.2009.29.4.377.
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