A method for solving basic boundary value problems for a second-order self-adjoint differential operator with constant coefficients in domains of arbitrary shape

2021 ◽  
Vol 1 (1) ◽  
pp. 12-22
Author(s):  
I.S. Makarova
Keyword(s):  
Differential Operator ◽  
Boundary Value Problems ◽  
Arbitrary Shape ◽  
Boundary Value ◽  
Second Order ◽  
Constant Coefficients ◽  
Basic Boundary

scholarly journals Second order elliptic boundary value problems in spaces with homogeneous norms

1980 ◽  
Vol 29 (1) ◽  
pp. 1-13 ◽  
Author(s):  
A. J. Pryde
Keyword(s):  
Boundary Value Problems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Partial Differential Operator ◽  
Second Order ◽  
Elliptic Boundary Value ◽  
First Order ◽  
Constant Coefficients ◽  
Regularity Results ◽  
Homogeneous Norms

AbstractWe consider the interior and Dirichiet problems and problems with first order boundary conditions, for a second order homogeneous elliptic partial differential operator with constant coefficients. Under natural conditions on the operators, these problems give rise to isomorphisms between the appropriate spaces with homogeneous norms. From there we obtain a priori estimates and regularity results for boundary value problems in Sobolev spaces.

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