This article is cited in 2 papers

Compact-analytical properties of variational functional in Sobolev spaces $W^{1,p}$

I. V. Orlov

Faculty of Mathematics and Informatics, V. Vernadsky Taurida National University, Simferopol, Ukraine

Abstract: In the work, conditions of welldefiniteness, compact continuity, compact differentiability and multiple compact differentiability of the Euler–Lagrange one-dimensional variational functional in Sobolev–Bochner spaces $W^{1,p}([a;b],F)$ are obtained in terms of belonging of the integrand to the corresponding Weierstrass pseudopolynomial classes.

Keywords and phrases: variational functional, integrand, Sobolev space, compact continuity, compact differentiability, dominating mixed smoothness, pseudopolynomial.

MSC: 49J05, 49L99

Received: 14.09.2011

Language: English

Bibliographic databases:

• 
•