This paper presents a necessary and sufficient condition on the convex function f in order that continuous solutions to minimize ∫ f(∥∇u(x)∥)dx on u0 + W01,1(Ω) satisfy a Strong Maximum Principle on any open connected Ω.
Cellina, A. (2002). On the strong maximum principle. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 130(2), 413-418 [10.1090/S0002-9939-01-06104-4].
On the strong maximum principle
Cellina, A
2002
Abstract
This paper presents a necessary and sufficient condition on the convex function f in order that continuous solutions to minimize ∫ f(∥∇u(x)∥)dx on u0 + W01,1(Ω) satisfy a Strong Maximum Principle on any open connected Ω.
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