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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On an elliptic boundary value problem not in divergence form

Author: Nguyên Phuong Các
Journal: Proc. Amer. Math. Soc. 88 (1983), 47-52
MSC: Primary 35P15; Secondary 35J25
MathSciNet review: 691277
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Abstract: Let $ G$ be a bounded domain in $ {R^n}(n \geqslant 2)$ with smooth boundary $ \partial G$. We consider the boundary value problem $ Mu - cu = f$ on $ G$, $ u = 0$ on $ \partial G$, where $ M$ is an elliptic differential operator not in divergence form. We discuss the characterization of the first eigenvalue $ {\lambda _0}$ of $ M$ and the solvability of the boundary value problem in terms of the relationship between $ c( \cdot )$ and $ {\lambda _0}$.

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Keywords: First eigenvalue, solvability of boundary value problem
Article copyright: © Copyright 1983 American Mathematical Society

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