TY - JOUR
T1 - Regular boundary value problems for complete second order elliptic differential-operator equations in UMD Banach spaces
AU - Favini, Angelo
AU - Shakhmurov, Veli
AU - Yakubov, Yakov
N1 - Funding Information:
The first author is a member of G.N.A.M.P.A. and the paper fits the 60% research program of G.N.A.M.P.A.-I.N.D.A.M.; The third author was supported by the Israel Ministry of Absorption.
PY - 2009/8
Y1 - 2009/8
N2 - 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.
AB - 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.
KW - Abstract elliptic equation
KW - Elliptic boundary problem
KW - Fredholmness
KW - Isomorphism
KW - R-sectorial operator
KW - UMD Banach space
UR - http://www.scopus.com/inward/record.url?scp=76349110999&partnerID=8YFLogxK
U2 - 10.1007/s00233-009-9138-0
DO - 10.1007/s00233-009-9138-0
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:76349110999
SN - 0037-1912
VL - 79
SP - 22
EP - 54
JO - Semigroup Forum
JF - Semigroup Forum
IS - 1
ER -