On elliptic problems with a nonlinearity depending on the gradient
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 \(1 \leq m \lt 2\).
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AGH Univeristy of Science and Technology Press
2009-01-01
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| Series: | Opuscula Mathematica |
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| Online Access: | http://www.opuscula.agh.edu.pl/vol29/4/art/opuscula_math_2929.pdf |
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doaj-42cdb2e2386f4427ab78f3c1c03deded2020-11-24T22:37:35ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742009-01-01294377391http://dx.doi.org/10.7494/OpMath.2009.29.4.3772929On elliptic problems with a nonlinearity depending on the gradientJan Chabrowski0University of Queensland, Department of Mathematics, St. Lucia 4072, Qld, AustraliaWe 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 \(1 \leq m \lt 2\).http://www.opuscula.agh.edu.pl/vol29/4/art/opuscula_math_2929.pdfNeumann problemnonlinearity depending on the gradient\(L^1\) data |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Jan Chabrowski |
| spellingShingle |
Jan Chabrowski On elliptic problems with a nonlinearity depending on the gradient Opuscula Mathematica Neumann problem nonlinearity depending on the gradient \(L^1\) data |
| author_facet |
Jan Chabrowski |
| author_sort |
Jan Chabrowski |
| title |
On elliptic problems with a nonlinearity depending on the gradient |
| title_short |
On elliptic problems with a nonlinearity depending on the gradient |
| title_full |
On elliptic problems with a nonlinearity depending on the gradient |
| title_fullStr |
On elliptic problems with a nonlinearity depending on the gradient |
| title_full_unstemmed |
On elliptic problems with a nonlinearity depending on the gradient |
| title_sort |
on elliptic problems with a nonlinearity depending on the gradient |
| publisher |
AGH Univeristy of Science and Technology Press |
| series |
Opuscula Mathematica |
| issn |
1232-9274 |
| publishDate |
2009-01-01 |
| description |
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 \(1 \leq m \lt 2\). |
| topic |
Neumann problem nonlinearity depending on the gradient \(L^1\) data |
| url |
http://www.opuscula.agh.edu.pl/vol29/4/art/opuscula_math_2929.pdf |
| work_keys_str_mv |
AT janchabrowski onellipticproblemswithanonlinearitydependingonthegradient |
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1725716455018725376 |