Displaying similar documents to “Microlocal analysis in the dual of a Colombeau algebra: generalized wave front sets and noncharacteristic regularity.”

On the unique extension problem for functionals of the calculus of variations

Luciano Carbone, Riccardo De Arcangelis (2001)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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By drawing inspiration from the treatment of the non parametric area problem, an abstract functional is considered, defined for every open set in a given class of open subsets of R n and every function in C R n , and verifying suitable assumptions of measure theoretic type, of invariance, convexity, and lower semicontinuity. The problem is discussed of the possibility of extending it, and of the uniqueness of such extension, to a functional verifying analogous properties, but defined in wider...