Linear and nonlinear abstract elliptic equations with VMO coefficients and applications

被引：0
作者：
Veli B 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：
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摘要：
In this paper, maximal regularity properties for linear and nonlinear elliptic differential-operator equations with VMO (vanishing mean oscillation) coefficients are studied. For linear case, the uniform separability properties for 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 nonlinear equation is established. In application, the maximal regularity properties of the anisotropic elliptic equation and the system of equations with VMO coefficients are derived.
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[1]  
Sarason D(1975)On functions of vanishing mean oscillation Trans. Am. Math. Soc 207 391-405
[2]  
Chiarenza F(1991)Interior Ric. Mat 40 149-168
[3]  
Frasca M(1993) estimates for non divergence elliptic equations with discontinuous coefficients Trans. Am. Math. Soc 336 841-853
[4]  
Longo P(2007)-solvability of the Dirichlet problem for nondivergence elliptic equations with VMO coefficients Commun. Partial Differ. Equ 32 453-475
[5]  
Chiarenza F(2003)Parabolic and elliptic equations with VMO coefficients Numer. Funct. Anal. Optim 24 1-15
[6]  
Frasca M(2009)On well-posedeness of the nonlocal boundary value problem for elliptic equations Semigroup Forum 79 22-54
[7]  
Longo P(2003)Regular boundary value problems for complete second order elliptic differential-operator equations in UMD Banach spaces J. Evol. Equ 3 62-88
[8]  
Krylov NV(1964)Maximal Publ. Math 19 5-68
[9]  
Ashyralyev A(2012)-regularity for elliptic operators with Appl. Math. Comput 218 11952-11958
[10]  
Favini A(2012)-coefficients J. Optim. Theory Appl 154 491-499
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