Displaying similar documents to “Necessary conditions for weak lower semicontinuity on domains with infinite measure”

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...

About steady transport equation I – L p -approach in domains with smooth boundaries

Antonín Novotný (1996)

Commentationes Mathematicae Universitatis Carolinae

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We investigate the steady transport equation λ z + w · ∇ z + a z = f , λ > 0 in various domains (bounded or unbounded) with smooth noncompact boundaries. The functions w , a are supposed to be small in appropriate norms. The solution is studied in spaces of Sobolev type (classical Sobolev spaces, Sobolev spaces with weights, homogeneous Sobolev spaces, dual spaces to Sobolev spaces). The particular stress is put onto the problem to extend the results to as less regular vector fields w , a , as possible (conserving the requirement...