Boundedness of the extremal solution of some p-Laplacian problems
In this article we consider the p-Laplace equation on a smooth bounded domain of with zero Dirichlet boundary conditions. Under adequate assumptions on f we prove that the extremal solution of this problem is in the energy class independently of the domain. We also obtain Lq and W1,q estimates for s...
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| Format: | article |
| Language: | eng |
| Published: |
2007
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| Online Access: | http://hdl.handle.net/10316/4603 |
| Country: | Portugal |
| Oai: | oai:estudogeral.sib.uc.pt:10316/4603 |
| Summary: | In this article we consider the p-Laplace equation on a smooth bounded domain of with zero Dirichlet boundary conditions. Under adequate assumptions on f we prove that the extremal solution of this problem is in the energy class independently of the domain. We also obtain Lq and W1,q estimates for such a solution. Moreover, we prove its boundedness for some range of dimensions depending on the nonlinearity f. |
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