# A Priori Bounds for Solutions and Spectra of Robin Boundary Value Problems

## Author

**Norman Dancer** and **Daniel Daners**

## Status

Research Report 94-33

October 1994

## Abstract

We prove global bounds for weak solutions of Robin Boundary Value
Problems which just depend on an upper bound of the volume of the
domain rather than the particular geometry of the domain. We also show
that such estimates cannot be true for the Neumann Problem. We also
obtain a generalization of the classical Friedrichs inequality giving
a uniform positive lower bound on the spectrum of Robin Boundary Value
Problems.

## Key phrases

elliptic boundary value problems. a priori estimates. eigenvalue problems.

## AMS Subject Classification (1991)

Primary: 35J25

Secondary: 35B45, 35P15

## Content

The paper is available in the following forms:
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apri-robin.dvi (88kB)

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Sydney Mathematics and Statistics