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A Strong Maximum Principle for the Laplace Equation with Mixed Boundary Condition

✍ Scribed by Juan Dávila

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
121 KB
Volume
183
Category
Article
ISSN
0022-1236

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✦ Synopsis

In this work we present a comparison result for two solutions of the Laplace equation in a smooth bounded domain, satisfying the same mixed boundary condition (zero Dirichlet data on part of the boundary and zero Neumann data on the rest). The result is in some sense a generalization of the Hopf lemma to the case of mixed boundary conditions, where the barrier function is not given explicitly, but as the solution of the Laplace equation with a constant right hand side and mixed boundary condition 2001 Academic Press | 0 {u {.= | 0 f. for all . # H. Let v denote the solution of { &2v=1 in 0

(2) v=0

on

on 1 2 .

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