On fundamental solutions of elliptic systems

1968 ◽  
pp. 143-168
Author(s):  
M. I. Matiĭčuk ◽  
S. D. Èĭdel′man
Keyword(s):  
Elliptic Systems ◽  
Fundamental Solutions

scholarly journals On regularization of the Cauchy problem for elliptic systems in weighted Sobolev spaces

2019 ◽  
Vol 27 (6) ◽  
pp. 815-834
Author(s):  
Yulia Shefer ◽  
Alexander Shlapunov
Keyword(s):  
Cauchy Problem ◽  
Sobolev Spaces ◽  
Integral Formula ◽  
Weighted Sobolev Spaces ◽  
Elliptic Systems ◽  
Fundamental Solutions ◽  
Type Integral ◽  
The Cauchy Problem ◽  
Ill Posed ◽  
Neumann Type

AbstractWe consider the ill-posed Cauchy problem in a bounded domain{\mathcal{D}}of{\mathbb{R}^{n}}for an elliptic differential operator{\mathcal{A}(x,\partial)}with data on a relatively open subsetSof the boundary{\partial\mathcal{D}}. We do it in weighted Sobolev spaces{H^{s,\gamma}(\mathcal{D})}containing the elements with prescribed smoothness{s\in\mathbb{N}}and growth near{\partial S}in{\mathcal{D}}, controlled by a real number γ. More precisely, using proper (left) fundamental solutions of{\mathcal{A}(x,\partial)}, we obtain a Green-type integral formula for functions from{H^{s,\gamma}(\mathcal{D})}. Then a Neumann-type series, constructed with the use of iterations of the (bounded) integral operators applied to the data, gives a solution to the Cauchy problem in{H^{s,\gamma}(\mathcal{D})}whenever this solution exists.

DEGENERATE ELLIPTIC SYSTEMS OF CLASS I

1987 ◽  
Vol 7 (1) ◽  
pp. 97-108
Author(s):  
Zhibing Deng
Keyword(s):  
Elliptic Systems ◽  
Class I ◽  
Degenerate Elliptic

Improved geometric modeling using the method of fundamental solutions

2021 ◽  
Vol 130 ◽  
pp. 49-57
Author(s):  
C.S. Chen ◽  
Lionel Amuzu ◽  
Kwesi Acheampong ◽  
Huiqing Zhu
Keyword(s):  
Geometric Modeling ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions
Sign in / Sign up

Export Citation Format

Share Document