scholarly journals Lower bounds of solutions of general boundary value problems for differential operators with constant coefficients in a half-space

1982 ◽  
Vol 8 (2) ◽  
pp. 343-382
Author(s):  
Yoshihiro SHIBATA
Keyword(s):  
Boundary Value Problems ◽  
Half Space ◽  
Lower Bounds ◽  
Differential Operators ◽  
Boundary Value ◽  
General Boundary ◽  
Constant Coefficients

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

1981 ◽  
Vol 31 (1) ◽  
pp. 92-113 ◽  
Author(s):  
A. J. Pryde
Keyword(s):  
Boundary Value Problems ◽  
Differential Operators ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
A Priori ◽  
Elliptic Boundary Value ◽  
Partial Differential Operators ◽  
Constant Coefficients ◽  
Regularity Results ◽  
Homogeneous Norms

AbstractWe consider general boundary value problems for homogeneous elliptic partial differential operators with constant coefficients. Under natural conditions on the operators, these problems give rise to isomorphisms between the appropriate spaces with homogeneous norms. We also consider operators which are not properly elliptic and boundary systems which do not satisfy the complementing condition and determine when they give rise to left or right invertible operators. A priori inequalities and regularity results for the corresponding boundary value problems in Sobolev spaces are then readily obtained.

Recovering differential operators with two constant delays under Dirichlet/Neumann boundary conditions

2020 ◽  
Vol 28 (2) ◽  
pp. 237-241
Author(s):  
Biljana M. Vojvodic ◽  
Vladimir M. Vladicic
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Differential Operators ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions

AbstractThis paper deals with non-self-adjoint differential operators with two constant delays generated by {-y^{\prime\prime}+q_{1}(x)y(x-\tau_{1})+(-1)^{i}q_{2}(x)y(x-\tau_{2})}, where {\frac{\pi}{3}\leq\tau_{2}<\frac{\pi}{2}<2\tau_{2}\leq\tau_{1}<\pi} and potentials {q_{j}} are real-valued functions, {q_{j}\in L^{2}[0,\pi]}. We will prove that the delays and the potentials are uniquely determined from the spectra of four boundary value problems: two of them under boundary conditions {y(0)=y(\pi)=0} and the remaining two under boundary conditions {y(0)=y^{\prime}(\pi)=0}.

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