scholarly journals On non-elliptic boundary problems

1982 ◽  
Vol 86 ◽  
pp. 1-38
Author(s):  
Yoshio Kato
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Elliptic Differential Equation ◽  
Boundary Problems

The purpose of this paper is to study the boundary value problems for the second order elliptic differential equation

scholarly journals On a class of non-elliptic boundary problems

1974 ◽  
Vol 54 ◽  
pp. 7-20 ◽  
Author(s):  
Yoshio Kato
Keyword(s):  
Differential Equation ◽  
Bounded Domain ◽  
Elliptic Boundary ◽  
Second Order ◽  
Elliptic Differential Equation ◽  
Boundary Problems

Let Ω be a bounded domain in Rl (l ≥ 2) with, C∞ boundary Γ of dimension l — 1 and let there be given a second order elliptic differential equation(1) in Ω,where ∂j = ∂/∂xi and all coefficients are assumed, for the sake of simplicity, to be real-valued and C∞ on .

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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