Stampacchia–Caldéron–Zygmund theory for linear elliptic equations with discontinuous coefficients and singular drift

2019 ◽  
Vol 25 ◽  
pp. 47 ◽  
Author(s):  
Lucio Boccardo
Keyword(s):  
Boundary Value Problem ◽  
Elliptic Equations ◽  
Principal Part ◽  
Boundary Value ◽  
Discontinuous Coefficients ◽  
Singular Drift ◽  
The Matrix

In this paper, the existence and properties of solutions of the boundary value problem (1.4) are studied. No regularity assumptions on the coefficients of the matrixM(x) are used (in particular we do not require that the principal part is −Δ), no assumptions on the size of ||E||LNare needed.

On the Boundary Value Problem in A Dihedral Angle for Normally Hyperbolic Systems of First Order

1998 ◽  
Vol 5 (2) ◽  
pp. 121-138
Author(s):  
O. Jokhadze
Keyword(s):  
Partial Differential Equations ◽  
Boundary Value Problem ◽  
Principal Part ◽  
Hyperbolic Systems ◽  
Boundary Value ◽  
Three Dimensional ◽  
Order System ◽  
First Order ◽  
Dimensional Boundary ◽  
Class Of Functions

Abstract Some structural properties as well as a general three-dimensional boundary value problem for normally hyperbolic systems of partial differential equations of first order are studied. A condition is given which enables one to reduce the system under consideration to a first-order system with the spliced principal part. It is shown that the initial problem is correct in a certain class of functions if some conditions are fulfilled.

scholarly journals Radially symmetric solutions of a class of singular elliptic equations

1990 ◽  
Vol 33 (2) ◽  
pp. 169-180 ◽  
Author(s):  
Juan A. Gatica ◽  
Gaston E. Hernandez ◽  
P. Waltman
Keyword(s):  
Boundary Value Problem ◽  
Elliptic Equations ◽  
Boundary Value ◽  
Open Unit ◽  
Open Unit Ball ◽  
Singular Elliptic Equations ◽  
Existence Of Positive Solutions ◽  
Radially Symmetric Solutions ◽  
Image Position ◽  
Special Case

The boundary value problemis studied with a view to obtaining the existence of positive solutions in C1([0, 1])∩C2((0, 1)). The function f is assumed to be singular in the second variable, with the singularity modeled after the special case f(x, y) = a(x)y−p, p>0.This boundary value problem arises in the search of positive radially symmetric solutions towhere Ω is the open unit ball in ℝN, centered at the origin, Γ is its boundary and |x| is the Euclidean norm of x.

The Basic Mixed Plane Boundary Value Problem of Statics in the Elastic Mixture Theory

2000 ◽  
Vol 7 (3) ◽  
pp. 427-440 ◽  
Author(s):  
M. Basheleishvili ◽  
SH. Zazashvili
Keyword(s):  
Boundary Value Problem ◽  
Displacement Vector ◽  
Boundary Value ◽  
Mixture Theory ◽  
Special Kind ◽  
Singular Integral Equations ◽  
Discontinuous Coefficients ◽  
Plane Boundary ◽  
Stress Vector ◽  
Elastic Mixture

Abstract The basic mixed plane boundary value problem of equations of statics of the elastic mixture theory is considered in a simply connected domain when the displacement vector is given on one part of the boundary and the stress vector on the remaining part. The problem is investigated using the general displacement vector and stress vector representations obtained in [Basheleishvili, Georgian Math. J. 4: 223–242, 1997]. These representations enable us to reduce the considered problem to a system of singular integral equations with discontinuous coefficients of special kind. The solvability of this system in a certain class is proved, which implies that the basic plane boundary value problem has a solution and this solution is unique.

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