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On a unilateral problem associated with elliptic operators


Author: Peter Hess
Journal: Proc. Amer. Math. Soc. 39 (1973), 94-100
MSC: Primary 35J60
DOI: https://doi.org/10.1090/S0002-9939-1973-0328336-7
MathSciNet review: 0328336
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Abstract: Let $ \mathcal{A}$ be a uniformly elliptic linear differential expression of second order, defined on the bounded domain $ \Omega \subset {R^m}$, and let $ \beta \subset R \times R$ be a maximal monotone graph. Under some growth assumption on $ \beta $ it is shown that for any given $ f \in {L^2}(\Omega )$ the problem: $ \mathcal{A}u + \beta (u) \mathrel\backepsilon f$ on $ \Omega ,u = 0$ on $ \partial \Omega $, admits a strong solution. It is not required that $ \mathcal{A}$ is monotone.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0328336-7
Keywords: Uniformly elliptic linear differential operator, maximal monotone mapping, Yosida approximation, homotopy arguments, Sobolev space, strong solution
Article copyright: © Copyright 1973 American Mathematical Society