scholarly journals Integral representations of solutions of periodic elliptic equations

2007 ◽  
pp. 323-339
Author(s):  
Peter Kuchment
Keyword(s):  
Elliptic Equations ◽  
Integral Representations

24.—The Solution of Initial-Boundary Value Problems for Pseudoparabolic Partial Differential Equations

1976 ◽  
Vol 74 ◽  
pp. 311-326 ◽  
Author(s):  
William Rundell ◽  
I. N. Sneddon
Keyword(s):  
Partial Differential Equations ◽  
Fundamental Solution ◽  
Boundary Value Problems ◽  
Elliptic Equations ◽  
Boundary Value ◽  
Initial Boundary ◽  
Integral Representations ◽  
Initial Boundary Value Problems ◽  
Regularity Theorem ◽  
Initial Boundary Value

SynopsisA fundamental solution for equations of pseudoparabolic type is constructed by a method analogous to Hadamard's construction for elliptic equations. By the use of this fundamental solution we obtain a regularity theorem and integral representations for the solution to the more common initial boundary value problems that are associated with these equations.

The Dirichlet problem for the uniformly elliptic equation in generalized weighted Morrey spaces

2020 ◽  
Vol 57 (1) ◽  
pp. 68-90 ◽  
Author(s):  
Tahir S. Gadjiev ◽  
Vagif S. Guliyev ◽  
Konul G. Suleymanova
Keyword(s):  
Elliptic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Morrey Spaces ◽  
Smooth Bounded Domain ◽  
Weighted Morrey Spaces ◽  
Priori Estimates ◽  
Muckenhoupt Class ◽  
Morrey Estimates ◽  
Dirichlet Boundary Problem

Abstract In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝn are obtained.

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