Weak convergence in L1 of the sequences of monotonic functions

• Autorzy: Puchała P.
• Języki publikacji: EN

Abstrakty

EN

We use (quasi-) Young measures associated with strictly monotonic functions with a differentiable inverse to prove an L1 ([0,1],ℝ) weak convergence of the monotonic sequence of such functions. The result is well known, but the method seems to be new.

Słowa kluczowe

EN

mathematics; weak convergence; quasi-Young measures

PL

matematyka; zbieżność słaba

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2014
• Tom: Vol. 13, nr 3
• Strony: 195--199
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Puchała P.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

Bibliografia

• [1] Young L.C., Generalized curves and the existence of an attained absolute minimum in the calculus of variations, Comptes Rendus de la Société des Sciences et des Lettres de Varsovie, classe III 1937, 30, 212-234.
• [2] Puchała P., An elementary method of calculating an explicit form of Young measures in some special cases, in print.
• [3] Benedetto J.J., Czaja W., Integration and Modern Analysis, Birkhäuser, Boston, Basel, Berlin 2009.
• [4] Pedregal P., Variational Methods in Nonlinear Elasticity, SIAM, Philadelphia, USA 2000.
• [5] Roubíček T., Relaxation in Optimization Theory and Variational Calculus, Walter de Gruyter, Berlin, New York 1997.