Opuscula Math. 29, no. 4 (2009), 377-391

Opuscula Mathematica

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.

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  • Jan Chabrowski
  • University of Queensland, Department of Mathematics, St. Lucia 4072, Qld, Australia
  • Received: 2009-07-29.
  • Accepted: 2009-08-17.
Opuscula Mathematica - cover

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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