Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1983-0691277-6
MathSciNet review: 691277
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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}$.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35P15, 35J25

Retrieve articles in all journals with MSC: 35P15, 35J25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0691277-6
Keywords: First eigenvalue, solvability of boundary value problem
Article copyright: © Copyright 1983 American Mathematical Society