scholarly journals Regularity results for singular elliptic problems

2006 ◽  
Vol 4 (3) ◽  
pp. 243-259 ◽  
Author(s):  
Loredana Caso
Keyword(s):  
Boundary Conditions ◽  
Weight Function ◽  
Elliptic Equations ◽  
Global Regularity ◽  
Elliptic Problems ◽  
The Other ◽  
Weighted Spaces ◽  
Regularity Results

Some local and global regularity results for solutions of linear elliptic equations in weighted spaces are proved. Here the leading coefficients are VMO functions, while the hypotheses on the other coefficients and the boundary conditions involve a suitable weight function.

Existence and Regularity Results for Anisotropic Elliptic Problems

2009 ◽  
Vol 9 (2) ◽  
Author(s):  
Agnese Di Castro
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Elliptic Problems ◽  
Dirichlet Boundary Conditions ◽  
Bounded Domains ◽  
Existence And Regularity Results ◽  
Regularity Results ◽  
Homogeneous Dirichlet Boundary Conditions

AbstractWe study existence and regularity of the solutions for some anisotropic elliptic problems with homogeneous Dirichlet boundary conditions in bounded domains.

LINEAR ELLIPTIC PROBLEMS WITH MIXED BOUNDARY CONDITIONS RELATED TO RADIATION HEAT TRANSFER

2002 ◽  
Vol 12 (04) ◽  
pp. 541-565 ◽  
Author(s):  
MARIA MICHAELA PORZIO ◽  
ÓSCAR LÓPEZ-POUSO
Keyword(s):  
Boundary Conditions ◽  
Elliptic Equations ◽  
Mixed Boundary ◽  
Radiation Heat Transfer ◽  
Elliptic Problems ◽  
Mixed Boundary Conditions ◽  
Radiation Heat ◽  
Neumann Problems ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

We prove the existence and uniqueness results for elliptic problems with L1 data and mixed boundary conditions which include as particular cases the Dirichlet and the Neumann problems. These elliptic equations are related to radiation heat trasfer.

scholarly journals Global in Space Regularity Results for the Heat Equation with Robin-Neumann Type Boundary Conditions in Time-varying Domains

2019 ◽  
pp. 355-370
Author(s):  
Tahir Boudjeriou ◽  
Arezki Kheloufi
Keyword(s):  
Sobolev Space ◽  
Boundary Conditions ◽  
Heat Equation ◽  
Decomposition Method ◽  
Global Regularity ◽  
Domain Decomposition Method ◽  
Time Varying ◽  
Neumann Type ◽  
Type Boundary ◽  
Regularity Results

This article deals with the heat equation @tu @2x u = f in D; D = {(t; x) 2 R2 : a < t < b; (t) < x < +1} with the function satisfying some conditions and the problem is supplemented with boundary conditions of Robin-Neumann type. We study the global regularity problem in a suitable parabolic Sobolev space. We prove in particular that for f 2 L2(D) there exists a unique solution u such that u; @tu; @jx u 2 L2 (D) ; j = 1; 2: The proof is based on the domain decomposition method. This work complements the results obtained in [10].

scholarly journals Local versus nonlocal elliptic equations: short-long range field interactions

2020 ◽  
Vol 10 (1) ◽  
pp. 895-921
Author(s):  
Daniele Cassani ◽  
Luca Vilasi ◽  
Youjun Wang
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Principle ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Spectral Properties ◽  
Fractional Laplacian ◽  
Coupling Parameter ◽  
Nonlocal Operators ◽  
The Maximum Principle ◽  
Regularity Results

Abstract In this paper we study a class of one-parameter family of elliptic equations which combines local and nonlocal operators, namely the Laplacian and the fractional Laplacian. We analyze spectral properties, establish the validity of the maximum principle, prove existence, nonexistence, symmetry and regularity results for weak solutions. The asymptotic behavior of weak solutions as the coupling parameter vanishes (which turns the problem into a purely nonlocal one) or goes to infinity (reducing the problem to the classical semilinear Laplace equation) is also investigated.

Lower Bounds to the Eigenvalues in One-Dimensional Problems by a Shift in the Weight Function

1970 ◽  
Vol 37 (2) ◽  
pp. 267-270 ◽  
Author(s):  
D. Pnueli
Keyword(s):  
Lower Bound ◽  
Weight Function ◽  
Lower Bounds ◽  
Variational Formulation ◽  
Ritz Method ◽  
The Other ◽  
One Dimensional ◽  
Systematic Shift ◽  
The One ◽  
Detailed Computation

A method is presented to obtain both upper and lower bound to eigenvalues when a variational formulation of the problem exists. The method consists of a systematic shift in the weight function. A detailed procedure is offered for one-dimensional problems, which makes improvement of the bounds possible, and which involves the same order of detailed computation as the Rayleigh-Ritz method. The main contribution of this method is that it yields the “other bound;” i.e., the one which cannot be obtained by the Rayleigh-Ritz method.

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