Elliptic boundary value problems for general elliptic systems in complete scales of Banach spaces

1998 ◽  
pp. 231-241
Author(s):  
I. Roitberg
Keyword(s):  
Boundary Value Problems ◽  
Banach Spaces ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Systems ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value ◽  
General Elliptic ◽  
Scales Of Banach Spaces

scholarly journals The Sharpiro–Lopatinskij Condition for Elliptic Boundary Value Problems

2006 ◽  
Vol 9 ◽  
pp. 287-329 ◽  
Author(s):  
Katsiaryna Krupchyk ◽  
Jukka Tuomela
Keyword(s):  
Boundary Value Problems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Systems ◽  
Formal Theory ◽  
Elliptic Boundary Value Problems ◽  
Constructive Method ◽  
Elliptic Boundary Value ◽  
The Given ◽  
Well Posed

AbstractElliptic boundary value problems are well posed in suitable Sobolev spaces, if the boundary conditions satisfy the Shapiro–Lopatinskij condition. We propose here a criterion (which also covers over-determined elliptic systems) for checking this condition. We present a constructive method for computing the compatibility operator for the given boundary value problem operator, which is also necessary when checking the criterion. In the case of two independent variables we give a formulation of the criterion for the Shapiro–Lopatinskij condition which can be checked in a finite number of steps. Our approach is based on formal theory of PDEs, and we use constructive module theory and polynomial factorisation in our test. Actual computations were carried out with computer algebra systems Singular and MuPad.

scholarly journals Nonnegative Solutions of a Nonlinear System and Applications to Elliptic BVPs*

2021 ◽  
pp. 15-26
Author(s):  
Guangchong Yang ◽  
Yanqiu Chen
Keyword(s):  
Fixed Point ◽  
Nonlinear System ◽  
Boundary Value Problems ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value ◽  
Nonnegative Solutions

Abstract In this communication, we study the existence of nonnegative solutions of a nonlinear system in Banach spaces. These maps involved in the system defined on cone do not necessarily take values in the cone. Using fixed point theorems just established for this type of mappings, nonnegative solutions of the system are obtained and used to investigate elliptic boundary value problems (BVPs). MSC(2010): 47H10, 35J57. Keywords: Nonlinear system, Nonnegative solutions, Nowhere normal-outward maps, Fixed point, Elliptic BVPs.

Sign in / Sign up

Export Citation Format

Share Document