An approximation theorem in higher order Orlicz-Sobolev spaces and applications
A. Benkirane, J.-P. Gossez (1989)
Studia Mathematica
Tomáš G. Roskovec, Filip Soudský (2023)
Kybernetika
The weak lower semicontinuity of the functional is a classical topic that was studied thoroughly. It was shown that if the function is continuous and convex in the last variable, the functional is sequentially weakly lower semicontinuous on . However, the known proofs use advanced instruments of real and functional analysis. Our aim here is to present a proof understandable even for students familiar only with the elementary measure theory.
Bennewitz, Christer, Saitō, Yoshimi (2002)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Nina A. Chernyavskaya, Leonid A. Shuster (2012)
Czechoslovak Mathematical Journal
El Baraka, Azzeddine (2002)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Alireza Ranjbar-Motlagh (2009)
Studia Mathematica
The purpose of this paper is to prove an embedding theorem for Sobolev type functions whose gradients are in a Lorentz space, in the framework of abstract metric-measure spaces. We then apply this theorem to prove absolute continuity and differentiability of such functions.
Augusto C. Ponce (2004)
Journal of the European Mathematical Society
Il'kiv, V.S., Ptashnik, B.I. (2005)
Sibirskij Matematicheskij Zhurnal
Neil Trudinger (1974)
Studia Mathematica
Francesca Crispo, Paolo Maremonti (2004)
Rendiconti del Seminario Matematico della Università di Padova
Kufner, Alois, Wannebo, Andreas (1995)
Georgian Mathematical Journal
Seppo Granlund (1982)
Mathematica Scandinavica
Andrea Cianchi, Luboš Pick (2010)
Annales de l’institut Fourier
We find an optimal Sobolev-type space on all of whose functions admit a trace on subspaces of of given dimension. A corresponding trace embedding theorem with sharp range is established.
Gérard Bourdaud, Madani Moussai, Winfried Sickel (2006)
Annales de l'I.H.P. Analyse non linéaire
P. Pietra (1982)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
S. Zaidman (1984)
Rendiconti del Seminario Matematico della Università di Padova
A. Jouini, P. G. Lemarie-Rieusset (1993)
Annales de l'I.H.P. Analyse non linéaire
Pierre Gilles Lemarie-Rieusset (1992)
Revista Matemática Iberoamericana
The notion of non-orthogonal multi-resolution analysis and its compatibility with differentiation (as expressed by the commutation formula) lead us to the construction of a multi-resolution analysis of L2(Rn)n which is well adapted to the approximation of divergence-free vector functions. Thus, we obtain unconditional bases of compactly supported divergence-free vector wavelets.
Li, Hengguang, Mazzucato, Anna, Nistor, Victor (2010)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
Steven G. Krantz (1979)
Mathematische Annalen