TY  - JOUR
ID  - Chabrowski2009
LB  - Chabrowski2009
AU  - Chabrowski, Jan
TI  - On elliptic problems with a nonlinearity depending on the gradient
ST  - On elliptic problems with a nonlinearity depending on the gradient
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2009
VL  - 29
IS  - 4
SP  - 377
EP  - 391
DO  - http://dx.doi.org/10.7494/OpMath.2009.29.4.377
UR  - http://dx.doi.org/10.7494/OpMath.2009.29.4.377
AB  - 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 \(1 \leq m \lt 2\).
KW  - Neumann problem
KW  - nonlinearity depending on the gradient
KW  - \(L^1\) data
SN  - 1232-9274
ER  -