In this work we give a result concerning the continuous dependence on the data for weak solutions of a class of semilinear elliptic variationalinequalities(Pn) 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 C1,α-weak solutions of problem (Pn) found in Matzeu and Servadei (2010) [9] through variational techniques. To be precise, we show that the solutions of (Pn), 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.
Matzeu, M., Servadei, R. (2011). Stability for semilinear variational inequalities depending on the gradient. NONLINEAR ANALYSIS, 74(15), 5161-5170 [10.1016/j.na.2011.05.010].
Stability for semilinear variational inequalities depending on the gradient
MATZEU, MICHELE;
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 variationalinequalities(Pn) 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 C1,α-weak solutions of problem (Pn) found in Matzeu and Servadei (2010) [9] through variational techniques. To be precise, we show that the solutions of (Pn), 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.Questo articolo è pubblicato sotto una Licenza Licenza Creative Commons
