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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the singular boundary value problem for elliptic equations


Author: Kazunari Hayashida
Journal: Trans. Amer. Math. Soc. 184 (1973), 205-221
MSC: Primary 35J25
DOI: https://doi.org/10.1090/S0002-9947-1973-0328320-8
MathSciNet review: 0328320
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Abstract: The operator $ \mathcal{L}$ is elliptic and of second order in a domain $ \Omega $ in $ {R^N}$. We consider the following boundary value problem: $ \mathcal{L}u = f$ in $ \Omega $ and $ \mathcal{B}u = 0$ on $ \partial \Omega $, where $ \mathcal{B} = ad/dn + \beta $ (d/dn is the conormal derivative on $ \partial \Omega $). The coefficient $ \alpha $ is assumed to be nonnegative. However, $ \alpha $ may vanish partly on $ \partial \Omega $. Then the regularity of the weak solutions for the above problem is shown by the variational method.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0328320-8
Keywords: Elliptic operator, boundary operator, regularity problem, elliptic regularization, Sobolev space, variational method
Article copyright: © Copyright 1973 American Mathematical Society