scholarly journals Study of the initial value problems appearing in a method of factorization of second-order elliptic boundary value problems

2008 ◽  
Vol 68 (10) ◽  
pp. 2984-3008 ◽  
Author(s):  
J. Henry ◽  
A.M. Ramos
Keyword(s):  
Boundary Value Problems ◽  
Initial Value Problems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Elliptic Boundary Value Problems ◽  
Initial Value ◽  
Elliptic Boundary Value

General edge asymptotics of solutions of second-order elliptic boundary value problems I

1993 ◽  
Vol 123 (1) ◽  
pp. 109-155 ◽  
Author(s):  
Martin Costabel ◽  
Monique Dauge
Keyword(s):  
Boundary Value Problems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Weighted Sobolev Spaces ◽  
Second Order ◽  
Elliptic Boundary Value Problems ◽  
General Situation ◽  
Opening Angle ◽  
Elliptic Boundary Value ◽  
Basic Facts

SynopsisThis is the first of two papers in which we study the singularities of solutions of second-order linear elliptic boundary value problems at the edges of piecewise analytic domains in ℝ3. When the opening angle at the edge is variable, there appears the phenomenon of “crossing” of the exponents of singularities. For this case, we introduce the appropriate combinations of the simple tensor product singularities that allow us to give estimates in ordinary and weighted Sobolev spaces for the regular part of the solution and for the coefficients of the singularities. These combinations appear in a natural way as sections of an analytic bundle above the edge. Their behaviour is described with the help of divided differences of powers of the distance to the edge. The class of operators considered includes second-order elliptic operators with analytic complex-valued coefficients with mixed Dirichlet, Neumann or oblique derivative conditions. With our description of the singularities we are able to remove some restrictive hypotheses that were previously made in other works. In this first part, we prove the basic facts in a simplified framework. Nevertheless the tools we use are essentially the same in the general situation.

scholarly journals Fundamental solutions and surface distributions

1969 ◽  
Vol 16 (3) ◽  
pp. 255-257
Author(s):  
R. A. Adams ◽  
G. F. Roach
Keyword(s):  
Elliptic Equation ◽  
Boundary Value Problems ◽  
Bounded Domain ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Fundamental Solutions ◽  
Second Order ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value ◽  
Image Position

When studying the solutions of elliptic boundary value problems in a bounded, smoothly bounded domain D⊂Rn we often encounter the formulawhere u(x)∈C2(D)∩C′(D̄) is a solution of the second order self-adjoint elliptic equationand denotes differentiation along the inward normal to ∂D at x∈∂D.

Sign in / Sign up

Export Citation Format

Share Document