Regular boundary value problems for complete second order elliptic differential-operator equations in UMD Banach spaces

被引:0
作者
Angelo Favini
Veli Shakhmurov
Yakov Yakubov
机构
[1] Universita di Bologna,Dipartimento di Matematica
[2] Okan University,Department of Mathematics Akfirat
[3] Tel-Aviv University,Raymond and Beverly Sackler School of Mathematical Sciences
来源
Semigroup Forum | 2009年 / 79卷
关键词
Abstract elliptic equation; Elliptic boundary problem; Banach space; -sectorial operator; Isomorphism; Fredholmness;
D O I
暂无
中图分类号
学科分类号
摘要
We consider coerciveness and Fredholmness of nonlocal boundary value problems for complete second order elliptic differential-operator equations in UMD Banach spaces. In some special cases, the main coefficients of the boundary conditions may be bounded operators and not only complex numbers. Then, we prove an isomorphism, in particular, maximal Lp-regularity, of the problem with a linear parameter in the equation. In both cases, the boundary conditions may also contain unbounded operators in perturbation terms. Finally, application to regular nonlocal boundary value problems for elliptic equations of the second order in non-smooth domains are presented. Equations and boundary conditions may contain differential-integral parts. The spaces of solvability are Sobolev type spaces Wp,q2,2.
引用
收藏
页码:22 / 54
页数:32
相关论文
共 33 条
[1]  
Agmon S.(1962)On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems Commun. Pure Appl. Math. 15 119-147
[2]  
Agmon S.(1963)Properties of solutions of ordinary differential equations in Banach spaces Commun. Pure Appl. Math. 16 121-239
[3]  
Nirenberg L.(1964)Elliptic problems with a parameter and parabolic problems of general type Usp. Mat. Nauk 19 53-161
[4]  
Agranovich M.S.(2006)Maximal J. Evol. Equ. 6 773-790
[5]  
Vishik M.I.(1983)-regularity for parabolic and elliptic equations on the line Ark. Mat. 21 163-168
[6]  
Arendt W.(2004)Some remarks on Banach spaces in which martingale difference sequences are unconditional Math. Ann. 328 545-583
[7]  
Duelli M.(1964)New thoughts on old results of R.T. Seeley Rend. Semin. Mat. Univ. Padova 34 157-162
[8]  
Bourgain J.(1987)Un’applicazione della teoria degli integrali singolri allo studio delle equazioni differenziali astratta del primo ordine Math. Z. 196 270-286
[9]  
Denk R.(2008)On the closedness of the sum of two closed operators Differ. Integral Equ. 21 497-512
[10]  
Dore G.(2004)Higher order ordinary differential-operator equations on the whole axis in UMD Banach spaces Funkc. Ekvacioj 47 423-452