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Transactions of the American Mathematical Society

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Robin boundary value problems on arbitrary domains


Author: Daniel Daners
Journal: Trans. Amer. Math. Soc. 352 (2000), 4207-4236
MSC (2000): Primary 35J25; Secondary 35D10, 35B45
Published electronically: March 21, 2000
MathSciNet review: 1650081
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Abstract:

We develop a theory of generalised solutions for elliptic boundary value problems subject to Robin boundary conditions on arbitrary domains, which resembles in many ways that of the Dirichlet problem. In particular, we establish $L_p$-$L_q$-estimates which turn out to be the best possible in that framework. We also discuss consequences to the spectrum of Robin boundary value problems. Finally, we apply the theory to parabolic equations.


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Additional Information

Daniel Daners
Affiliation: School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia
Email: D.Daners@maths.usyd.edu.au

DOI: https://doi.org/10.1090/S0002-9947-00-02444-2
Received by editor(s): April 5, 1996
Received by editor(s) in revised form: May 19, 1998
Published electronically: March 21, 2000
Additional Notes: Supported by a grant of the Australian Research Council
Article copyright: © Copyright 2000 American Mathematical Society