Robin boundary value problems on arbitrary domains


Daniel Daners


Research Report 96-12
25 March 1996


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


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