In this work we give a result concerning the continuous dependence on the data for weak solutions of a class of semilinear elliptic variational inequalities (P(n)) with a nonlinear term depending on the gradient of the solution. This paper can be seen as the second part of the work Matzeu and Servadei (2010) [9], in the sense that here we give a stability result for the C(1,alpha)-weak solutions of problem (P(n)) found in Matzeu and Servadei (2010) [9] through variational techniques. To be precise, we show that the solutions of (P(n)), found with the arguments of Matzeu and Servadei (2010) [9], converge to a solution of the limiting problem (P), under suitable convergence assumptions on the data. (C) 2011 Elsevier Ltd. All rights reserved.

Stability for semilinear elliptic variational inequalities depending on the gradient

SERVADEI, RAFFAELLA
2011-01-01

Abstract

In this work we give a result concerning the continuous dependence on the data for weak solutions of a class of semilinear elliptic variational inequalities (P(n)) with a nonlinear term depending on the gradient of the solution. This paper can be seen as the second part of the work Matzeu and Servadei (2010) [9], in the sense that here we give a stability result for the C(1,alpha)-weak solutions of problem (P(n)) found in Matzeu and Servadei (2010) [9] through variational techniques. To be precise, we show that the solutions of (P(n)), found with the arguments of Matzeu and Servadei (2010) [9], converge to a solution of the limiting problem (P), under suitable convergence assumptions on the data. (C) 2011 Elsevier Ltd. All rights reserved.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11576/2626820
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