Stability for semilinear elliptic variational inequalities depending on the gradient

• Published in: Nonlinear analysis Vol. 74; no. 15; pp. 5161 - 5170
• Main Authors: Matzeu, Michele, Servadei, Raffaella
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.10.2011; Elsevier
• Subjects: Calculus of variations and optimal control; Constraining; Convergence; Critical point theory; Exact sciences and technology; Global analysis, analysis on manifolds; Gradient-dependent nonlinearity; Inequalities; Iterative techniques; Mathematical analysis; Mathematics; Nonlinearity; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in mathematical programming, optimization and calculus of variations; Numerical methods in optimization and calculus of variations; Partial differential equations; Penalization method; Sciences and techniques of general use; Semilinear elliptic variational inequalities; Stability; Stability result; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Variational methods; secondary; Semilinear elliptic variational inequalities; Stability result; Critical point theory; Penalization method; Variational methods; Gradient-dependent nonlinearity; Iterative techniques; primary; secondary 58E05; Nonlinear analysis; Iterative method; Critical point; primary 35J85; Variational inequality; 49J40; Nonlinearity; Mathematical model; Numerical stability
• ISSN: 0362-546X; 1873-5215
• DOI: 10.1016/j.na.2011.05.010

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 , α -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.