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Nonlinear Elliptic Variational Inequalities
Author(s) -
Bose Deb K.,
Brill Heinz
Publication year - 1979
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19790910108
Subject(s) - mathematics , bounded function , nonlinear system , monotone polygon , variational inequality , compact space , constraint (computer aided design) , class (philosophy) , pure mathematics , operator (biology) , mathematical analysis , geometry , biochemistry , chemistry , physics , repressor , quantum mechanics , artificial intelligence , computer science , transcription factor , gene
We 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 H 2 (Ω) solution lying between a given subsolution φ 1 and a given supersolution φ 2 ≧φ 1 , when Ω is bounded, and a H 1 (Ω) solution when Ω is unbounded.