Optimal regular differential operators with variable coefficients and applications

被引：0
作者：
Veli Shakhmurov
机构：
[1] Okan University,Department of Mechanical Engineering
来源：
Fixed Point Theory and Applications | / 2013卷
关键词：
differential equations with ; coefficients; boundary value problems; differential-operator equations; maximal ; regularity; abstract function spaces; nonlinear elliptic equations;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, maximal regularity properties for linear and nonlinear high-order elliptic differential-operator equations with VMO coefficients are studied. For the linear case, the uniform coercivity property of parameter-dependent boundary value problems is obtained in Lp spaces. Then, the existence and uniqueness of a strong solution of the boundary value problem for a high-order nonlinear equation are established. In application, the maximal regularity properties of the anisotropic elliptic equation and the system of equations with VMO coefficients are derived.
引用
收藏
相关论文
共 32 条
[1]  
Sarason D(1975)On functions of vanishing mean oscillation Trans. Am. Math. Soc 207 391-405
[2]  
Chiarenza F(1993)-solvability of the Dirichlet problem for nondivergence elliptic equations with VMO coefficients Trans. Am. Math. Soc 336 841-853
[3]  
Frasca M(1991)Interior Ric. Mat 40 149-168
[4]  
Longo P(2007) estimates for non divergence elliptic equations with discontinuous coefficients Commun. Partial Differ. Equ 32 453-475
[5]  
Chiarenza F(2006)Parabolic and elliptic equations with VMO coefficients Math. Ann 336 617-637
[6]  
Frasca M(2012)Applications of the differential calculus to nonlinear elliptic operators with discontinuous coefficients Appl. Math. Comput 218 11952-11958
[7]  
Longo P(2012)Necessary and sufficient condition for VMO function J. Optim. Theory Appl 154 491-499
[8]  
Krylov NV(2003)Embeddings for Morrey-Lorentz spaces J. Evol. Equ 3 62-88
[9]  
Palagachev DK(2003)Maximal Numer. Funct. Anal. Optim 24 1-15
[10]  
Recke L(1964)-regularity for elliptic operators with VMO-coefficients Publ. Math 19 5-68
1234