Diffeomorphic approximation of planar Sobolev homeomorphisms in Orlicz Sobolev spaces

被引：10

作者：

Campbell, Daniel ^{[1
]}

机构：

[1] Univ Erlangen Nurnberg, Dept Math, Cauerstr 11, D-91058 Erlangen, Germany

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2017年 / 273卷 / 01期

关键词：

Homeomorphisms; Approximation; Sobolev-Orlicz spaces; PIECEWISE AFFINE HOMEOMORPHISMS;

D O I：

10.1016/j.jfa.2017.03.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Omega subset of R-2 be a domain, let Phi be a Delta(2) Young function and let f is an element of W-1,W-Phi(Omega, R-2) be a homeomorphism between Omega and f(Omega). Then there exists a sequence of diffeomorphisms f(k) converging to f in the Sobolev-Orlicz space W-1,W-Phi(Omega, R-2). Further for an injective continuous map phi is an element of W-1,W-Phi (partial derivative(-1,1)(2), R-2) we find a diffeomorphism in W-1,W-Phi((-1,1)(2), R-2) that equals phi on the boundary. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：125 / 205

页数：81

共 19 条

[1] SEMICONTINUITY PROBLEMS IN THE CALCULUS OF VARIATIONS [J].

ACERBI, E ;

FUSCO, N .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1984, 86 (02) :125-145

[2]

[Anonymous], PREPRINT

[3]

Ball JM, 2010, CISM COUR L, V516, P1

[4] DISCONTINUOUS EQUILIBRIUM SOLUTIONS AND CAVITATION IN NON-LINEAR ELASTICITY [J].

BALL, JM .

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1982, 306 (1496) :557-611

[5]

Ball JM, 2001, LOND MATH S, V284, P1

[6]

BALL JM, 1977, ARCH RATION MECH AN, V63, P337, DOI 10.1007/BF00279992

[7]

Bellido JC, 2011, HOUSTON J MATH, V37, P449

[8]

Charles B., 1952, PAC J MATH, V2, P25, DOI DOI 10.2140/PJM.1952.2.25)

[9]

Gehring FW., 1959, Ann. Acad. Sci. Fenn. Ser. A I, V272, P1

[10]

Hencl S, 2014, LECT NOTES MATH, V2096, P1, DOI 10.1007/978-3-319-03173-6

← 1 2 →