scholarly journals Degenerate Differential Operators with Parameters

2007 ◽  
Vol 2007 ◽  
pp. 1-27 ◽  
Author(s):  
Veli B. Shakhmurov
Keyword(s):  
Boundary Value Problems ◽  
Differential Operators ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Cylindrical Domain ◽  
Nonlocal Boundary Value Problems ◽  
Degenerate Elliptic ◽  
Systems Of Elliptic Equations ◽  
Principal Parts ◽  
Degenerate Differential Operator

The nonlocal boundary value problems for regular degenerate differential-operator equations with the parameter are studied. The principal parts of the appropriate generated differential operators are non-self-adjoint. Several conditions for the maximal regularity uniformly with respect to the parameter and the Fredholmness in Banach-valuedLp−spaces of these problems are given. In applications, the nonlocal boundary value problems for degenerate elliptic partial differential equations and for systems of elliptic equations with parameters on cylindrical domain are studied.

scholarly journals Maximal regular boundary value problems in Banach-valued function spaces and applications

2006 ◽  
Vol 2006 ◽  
pp. 1-26 ◽  
Author(s):  
Veli B. Shakhmurov
Keyword(s):  
Boundary Value Problems ◽  
Differential Operators ◽  
Maximal Regularity ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Initial Boundary ◽  
Cylindrical Domain ◽  
Initial Boundary Value Problems ◽  
Nonlocal Boundary Value Problems ◽  
Initial Boundary Value

The nonlocal boundary value problems for differential operator equations of second order with dependent coefficients are studied. The principal parts of the differential operators generated by these problems are non-selfadjoint. Several conditions for the maximal regularity and the Fredholmness in Banach-valuedLp-spaces of these problems are given. By using these results, the maximal regularity of parabolic nonlocal initial boundary value problems is shown. In applications, the nonlocal boundary value problems for quasi elliptic partial differential equations, nonlocal initial boundary value problems for parabolic equations, and their systems on cylindrical domain are studied.

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