The green formula and H p spaces on trees

1995 ◽  
Vol 218 (1) ◽  
pp. 253-272 ◽  
Author(s):  
Fausto Di Biase ◽  
Massimo A. Picardello
Keyword(s):  
Green Formula ◽  
The Green Formula

scholarly journals The Method of Fischer-Riesz Equations for Elliptic Boundary Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
A. Alsaedy ◽  
N. Tarkhanov
Keyword(s):  
Boundary Value Problems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Cauchy Data ◽  
Adjoint Problem ◽  
Green Formula ◽  
Order System ◽  
Elliptic Boundary Value ◽  
The Given ◽  
The Green Formula

We develop the method of Fischer-Riesz equations for general boundary value problems elliptic in the sense of Douglis-Nirenberg. To this end we reduce them to a boundary problem for a (possibly overdetermined) first-order system whose classical symbol has a left inverse. For such a problem there is a uniquely determined boundary value problem which is adjoint to the given one with respect to the Green formula. On using a well-elaborated theory of approximation by solutions of the adjoint problem, we find the Cauchy data of solutions of our problem.

scholarly journals Integral Equations of the Linear Sloshing in an Infinite Chute and Their Discretization

2005 ◽  
Vol 5 (3) ◽  
pp. 259-275
Author(s):  
Mikhail M. Galanin ◽  
Tatiana V. Nizkaya
Keyword(s):  
Exact Solution ◽  
Finite Difference ◽  
Elliptic Equations ◽  
Auxiliary Problem ◽  
Green Formula ◽  
Finite Difference Schemes ◽  
Computational Domain ◽  
Order Of Accuracy ◽  
The Green Formula ◽  
Quadratic Order

AbstractIn this work we propose a new method for solving linear elliptic equations in an unbounded domain. The method is based on the representation of the exact solution as the sum of two functions. The former is the solution of some auxiliary problem and the latter can be found using the Green formula. Using finite-difference schemes, this method has a quadratic order of accuracy independent of the size of the computational domain, and in the 2D case requires O(N³) operations to find the solution, where N³ is the number of nodes within the computational domain. In the 3D case the method requires O(N^4) operations. Test computational examples showing the method's efficiency are given.

scholarly journals On Some Problems Generated by a Sesquilinear Form

2017 ◽  
Vol 63 (2) ◽  
pp. 278-315
Author(s):  
N D Kopachevskii ◽  
A R Yakubova
Keyword(s):  
Boundary Value Problems ◽  
Laplace Operator ◽  
Initial Boundary ◽  
The Other ◽  
Green Formula ◽  
Initial Boundary Value Problems ◽  
Dissipation Of Energy ◽  
Sesquilinear Form ◽  
Initial Boundary Value ◽  
The Laplace Operator

Based on the generalized Green formula for a sesquilinear nonsymmetric form for the Laplace operator, we consider spectral nonself-adjoint problems. Some of them are similar to classical problems while the other arise in problems of hydrodynamics, diffraction, and problems with surface dissipation of energy. Properties of solutions of such problems are considered. Also we study initial-boundary value problems generating considered spectral problems and prove theorems on correct solvability of such problems on any interval of time.

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