# Robin boundary value problems on arbitrary domains

## Author

**Daniel Daners**

## Status

Research Report 96-12

25 March 1996

## 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 Lp-Lq-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.

## Key phrases

boundary value problems. elliptic partial differential equations.

## AMS Subject Classification (1991)

Primary: 35J25

Secondary: 35K20, 35D05

## Content

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Sydney Mathematics and Statistics