scholarly journals A posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations

2013 ◽  
Vol 82 (283) ◽  
pp. 1543-1557 ◽  
Author(s):  
Yoshitaka Watanabe ◽  
Takehiko Kinoshita ◽  
Mitsuhiro T. Nakao
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Elliptic Partial Differential Equations ◽  
A Posteriori ◽  
Partial Differential ◽  
A Posteriori Estimates

scholarly journals On the rigorous foundations of the Fokas method for linear elliptic partial differential equations

2012 ◽  
Vol 468 (2141) ◽  
pp. 1325-1331 ◽  
Author(s):  
A. C. L. Ashton
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Complex Analysis ◽  
Boundary Value ◽  
Elliptic Partial Differential Equations ◽  
Unknown Boundary ◽  
Partial Differential ◽  
Global Relation ◽  
Fokas Method

In this paper, we address some of the rigorous foundations of the Fokas method, confining attention to boundary value problems for linear elliptic partial differential equations on bounded convex domains. The central object in the method is the global relation, which is an integral equation in the spectral Fourier space that couples the given boundary data with the unknown boundary values. Using techniques from complex analysis of several variables, we prove that a solution to the global relation provides a solution to the corresponding boundary value problem, and that the solution to the global relation is unique. The result holds for any number of spatial dimensions and for a variety of boundary value problems.

Sign in / Sign up

Export Citation Format

Share Document