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To appear on the Proceedings of the Symposium Year on Material Instabilities and Continuum Mechanics
 

Summary: To appear on the Proceedings of the Symposium Year on
Material Instabilities and Continuum Mechanics
An Approximation Lemma for W1,p
Functions
by Emilio Acerbi & Nicola Fusco
In this paper we give a direct proof of the following approximation result:
Theorem. Let Rn
be a regular open set, and p 1 . There exists a constant c such that, for every
u W1,p
() and every K > 0 there exists v W1,
() satisfying
v 1, K
meas{x: u(x) = v(x)} c
u p
1,p
Kp
.
Unlike several results of Luzin type available ([3],[4]), in this theorem we do not look for an approximating
function v which is close to u in the W1,p
norm, but we want a precise control on the gradient of v. Thus,

  

Source: Acerbi, Emilio - Dipartimento di Matematica, UniversitÓ degli Studi di Parma

 

Collections: Mathematics