The author considers the problem of global differentiability of solutions for a quasilinear, second order, Dirichlet problem relative to a bounded open subset $\Omega\subset{\Bbb R}^n$, $n>2$. Solutions here considered are Sobolev ones of the type $u\in H^1(\Omega,{\Bbb R}^N)$, and with the term global differentiable solutions are meant solutions of the type $u\in H^2(\Omega,{\Bbb R}^N)$. \par The main result is an existence theorem of solutions of such a type, under suitable conditions, and also a global second order estimate. The methodology adopted is in the framework of functional analysis, following some previous results by S. Campanato (see the quoted papers in references).

Global differentiability results for weak solutions of nonlinear elliptic problems with controlled growths / Fattorusso, Luisa Angela Maria. - In: JOURNAL OF NONLINEAR AND CONVEX ANALYSIS. - ISSN 1345-4773. - 7,:3(2006), pp. 411-422.

Global differentiability results for weak solutions of nonlinear elliptic problems with controlled growths

FATTORUSSO, Luisa Angela Maria
2006-01-01

Abstract

The author considers the problem of global differentiability of solutions for a quasilinear, second order, Dirichlet problem relative to a bounded open subset $\Omega\subset{\Bbb R}^n$, $n>2$. Solutions here considered are Sobolev ones of the type $u\in H^1(\Omega,{\Bbb R}^N)$, and with the term global differentiable solutions are meant solutions of the type $u\in H^2(\Omega,{\Bbb R}^N)$. \par The main result is an existence theorem of solutions of such a type, under suitable conditions, and also a global second order estimate. The methodology adopted is in the framework of functional analysis, following some previous results by S. Campanato (see the quoted papers in references).
2006
Global differentiability of weak solutions,elliptic problems; controlled growths; nonlinearity with q=2
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12318/5205
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