Nonlinear Elliptic Variational Inequalities
Copyright policy )Nonlinear Elliptic Variational Inequalities
AbstractWe consider the problem of finding a solution to a class of nonlinear elliptic variational inequalities. These inequalities may be defined on bounded or unbounded domains Ω, and the nonlinearity can depend on gradient terms. Appropriate definitions of sub‐and supersolutions relative to the constraint sets are given. By using a mixture of maximal monotone operator theory and compactness arguments we prove the existence of a H2(Ω) solution lying between a given subsolution φ1 and a given supersolution φ2≧φ1, when Ω is bounded, and a H1(Ω) solution when Ω is unbounded.
- Ruhr University Bochum Germany
Variational methods for higher-order elliptic equations, Equations involving nonlinear operators (general), nonlinearity, Variational inequalities, abstract existence theorem, Variational methods applied to PDEs, Fixed-point theorems, supersolution, subsolution, Leray-Schauder fixed point theorem, maximal monotone operators, Degree, winding number, Monotone operators and generalizations, nonlinear elliptic variational inequalities, perturbation theory
Variational methods for higher-order elliptic equations, Equations involving nonlinear operators (general), nonlinearity, Variational inequalities, abstract existence theorem, Variational methods applied to PDEs, Fixed-point theorems, supersolution, subsolution, Leray-Schauder fixed point theorem, maximal monotone operators, Degree, winding number, Monotone operators and generalizations, nonlinear elliptic variational inequalities, perturbation theory
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