ON SUPERPOSITION OPERATORS BETWEEN HIGHER-ORDER SOBOLEV SPACES AND A MULTIVARIATE FAA DI BRUNO FORMULA: THE SUBCRITICAL CASE

被引：0

作者：

Dinca, George ^{[1
]}

Isaia, Florin ^{[2
]}

机构：

[1] Univ Bucharest, Fac Math & Comp Sci, Bucharest 010014, Romania

[2] Transilvania Univ Brasov, Fac Math & Comp Sci, Brasov 500091, Romania

来源：

DIFFERENTIAL AND INTEGRAL EQUATIONS | 2013年 / 26卷 / 1-2期

关键词：

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, superposition operators, (N(g)u)(x) = g(u(x)), between two arbitrary Sobolev spaces are studied. Sufficient conditions which ensure the well-definedness, the continuity, and the validity of the higher-order chain rule for such operators are given in the subcritical case (see Remark 1.1). As a consequence of these properties, it is proved that N-g(W-m,W-p(Omega) boolean AND W-0(k,p)(Omega)) subset of W-0(l,q)(Omega).

引用

页码：11 / 58

页数：48

共 7 条

[1] Superposition Operators Between Higher-order Sobolev Spaces and a Multivariate Faa di Bruno Formula: Supercritical Case
Dinca, George
Isaia, Florin
ADVANCED NONLINEAR STUDIES, 2014, 14 (01) : 137 - 158
[2] On higher order angular derivatives - an application of Faa di Bruno's formula
Pan, Y.
Wang, M.
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2008, 53 (02) : 159 - 175
[3] Superposition operators between Sobolev spaces and a non-existence result of higher-order regular solutions for the p-Laplacian
Isaia, Florin
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 117 : 87 - 98
[4] ON THE SUPERPOSITION OPERATOR BETWEEN SOBOLEV SPACES: WELL-DEFINEDNESS, CONTINUITY, BOUNDEDNESS, AND HIGHER-ORDER CHAIN RULE
Isaia, Florin
HOUSTON JOURNAL OF MATHEMATICS, 2015, 41 (04): : 1277 - 1294
[5] Interior Schauder-Type Estimates for Higher-Order Elliptic Operators in Grand-Sobolev Spaces
Bilalov, Bilal T.
Sadigova, Sabina R.
SAHAND COMMUNICATIONS IN MATHEMATICAL ANALYSIS, 2021, 18 (02): : 129 - 148
[6] On the autonomous Nemytskii operator between Sobolev spaces in the critical and supercritical cases: Well-definedness and higher-order chain rule
Isaia, Florin
Nonlinear Analysis, Theory, Methods and Applications, 2022, 214
[7] On the autonomous Nemytskii operator between Sobolev spaces in the critical and supercritical cases: Well-definedness and higher-order chain rule
Isaia, Florin
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2022, 214

← 1 →