Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2001-12-31
Existence and Regularity Results for Non-Negative Solutions of some Semilinear Elliptic Variational Inequalities via Mountain Pass TechniquesMario Girardi, Loretta Mastroeni and Michele Matzeu (1) Università degli Studi di Roma Tre, Italy
(2) Università di Roma Tor Vergata, Italy
The main result stated in the present paper is the existence of a non-negative solution for a semilinear variational inequality through the use of some estimates for the Mountain-Pass critical points obtained for the penalized equations associated with the variational inequality. The positivity of the solution is achieved through a regularity result and the strong maximum principle.
Keywords: Semilinear variational inequalities, penalization method, Mountain-Pass theorem
Girardi Mario, Mastroeni Loretta, Matzeu Michele: Existence and Regularity Results for Non-Negative Solutions of some Semilinear Elliptic Variational Inequalities via Mountain Pass Techniques. Z. Anal. Anwend. 20 (2001), 845-857. doi: 10.4171/ZAA/1048