MAXIMUM-PRINCIPLES AND A PRIORI ESTIMATES FOR A CLASS OF PROBLEMS FROM NONLINEAR ELASTICITY

被引：45

作者：

BAUMAN, P ^{[1
]}

OWEN, NC ^{[1
]}

PHILLIPS, D ^{[1
]}

机构：

[1] UNIV SHEFFIELD,DEPT APPL & COMPUTAT MATH,SHEFFIELD S10 2TN,S YORKSHIRE,ENGLAND

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 1991年 / 8卷 / 02期

关键词：

NONLINEAR ELLIPTIC SYSTEM; ELASTIC MATERIAL;

D O I：

10.1016/S0294-1449(16)30269-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider smooth solutions, U, to the nonlinear elliptic system associated with a two dimensional elastic material which has energy functional [GRAPHICS] The function H (d) is nonnegative, convex and unbounded in a neighborhood of zero. Two maximum principles are proved for DU and we show that if OMEGA' subset-of subset-of OMEGA then parallel-to DU parallel-to C-alpha(OMEGA') and parallel-to DU-1 parallel-to L infinity (OMEGA') are bounded a priori in terms of parallel-to DU parallel-to L(p)(OMEGA) and W (U) for some p = p (H).

引用

下载

页码：119 / 157

页数：39

共 50 条

[41] DISCRETE POLYNOMIAL INTERPOLATION, GREEN-FUNCTIONS, MAXIMUM-PRINCIPLES, ERROR-BOUNDS AND BOUNDARY-VALUE-PROBLEMS
AGARWAL, RP
LALLI, BS
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1993, 25 (08) : 3 - 39
[42] A priori gradient estimates for bounded generalized solutions of a class of variational problems with linear growth
Bildhauer, M
JOURNAL OF CONVEX ANALYSIS, 2002, 9 (01) : 117 - 137
[43] A priori and a posteriori error analyses of augmented twofold saddle point formulations for nonlinear elasticity problems
Gatica, Gabriel N.
Marquez, Antonio
Rudolph, Walter
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2013, 264 : 23 - 48
[44] EXISTENCE THEOREMS, QUALITATIVE RESULTS AND A PRIORI BOUNDS FOR A CLASS OF NONLINEAR DIRICHLET PROBLEMS
BANDLE, C
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1975, 58 (03) : 219 - 238
[45] Nonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates
Cabre, Xavier
Sire, Yannick
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2014, 31 (01): : 23 - 53
[46] A PRIORI ESTIMATES TO THE MAXIMUM MODULUS OF GENERALIZED SOLUTIONS OF A CLASS OF QUASILINEAR ELLIPTIC EQUATIONS WITH ANISOTROPIC GROWTH CONDITIONS
梁廷
王向东
Applied Mathematics and Mechanics(English Edition), 1994, (11) : 1025 - 1034
[47] INTERIOR ESTIMATES FOR A CLASS OF REACTION-DIFFUSION SYSTEMS FROM L(1) A PRIORI ESTIMATES
HOLLIS, SL
MORGAN, J
JOURNAL OF DIFFERENTIAL EQUATIONS, 1992, 98 (02) : 260 - 276
[48] Maximum principles and symmetry results for a class of fully nonlinear elliptic PDEs
Enache, Cristian
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2010, 17 (05): : 591 - 600
[49] Maximum principles and bounds for a class of fourth order nonlinear elliptic equations
Mareno, A.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 377 (02) : 495 - 500
[50] Maximum principles and symmetry results for a class of fully nonlinear elliptic PDEs
Cristian Enache
Nonlinear Differential Equations and Applications NoDEA, 2010, 17 : 591 - 600

← 1 2 3 4 5 →