Opuscula Math. 29, no. 4 (2009), 377-391
http://dx.doi.org/10.7494/OpMath.2009.29.4.377

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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