scholarly journals Regularity results for fully nonlinear integro-differential operators with nonsymmetric positive kernels

2011 ◽  
Vol 139 (3-4) ◽  
pp. 291-319 ◽  
Author(s):  
Yong-Cheol Kim ◽  
Ki-Ahm Lee
Keyword(s):  
Differential Operators ◽  
Fully Nonlinear ◽  
Regularity Results ◽  
Positive Kernels

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.

scholarly journals Regularity for Fully Nonlinear Integro-differential Operators with Regularly Varying Kernels

2016 ◽  
Vol 44 (4) ◽  
pp. 673-705 ◽  
Author(s):  
Soojung Kim ◽  
Yong-Cheol Kim ◽  
Ki-Ahm Lee
Keyword(s):  
Differential Operators ◽  
Fully Nonlinear ◽  
Regularly Varying

Strongly elliptic boundary integral equations for electromagnetic transmission problems

1988 ◽  
Vol 109 (3-4) ◽  
pp. 271-296 ◽  
Author(s):  
Martin Costabel ◽  
Ernst P. Stephan
Keyword(s):  
Integral Equations ◽  
Differential Operators ◽  
Pseudodifferential Operators ◽  
Boundary Integral Equations ◽  
Elliptic Boundary ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Transmission Problems ◽  
Regularity Results ◽  
Electromagnetic Transmission

SynopsisWe study a boundary integral equation method for transmission problems for strongly elliptic differential operators, which yields a strongly elliptic system of pseudodifferential operators and which therefore can be used for numerical computations with Galerkin's procedure. The method is shown to work for the vector Helmholtz equation in ℝ3 with electromagnetic transmission conditions. We propose a slightly modified system of boundary values in order for the corresponding bilinear form to be coercive over H1. We analyse the boundary integral equations using the calculus of pseudodifferential operators. Here the concept of the principal symbol is used to derive existence and regularity results for the solution.

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