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


Norman Dancer and Daniel Daners


Research Report 94-33
October 1994


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


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