Stability for semilinear elliptic variational inequalities depending on the gradient |
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Authors: | Michele Matzeu |
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Institution: | a Dipartimento di Matematica, Università di Roma ‘Tor Vergata’, Via della Ricerca Scientifica, 00133 Roma, Italyb Dipartimento di Matematica, Università della Calabria, Ponte Pietro Bucci 31 B, 87036 Arcavacata di Rende (Cosenza), Italy |
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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 (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. |
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Keywords: | primary 35J85 49J40 secondary 58E05 |
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