scholarly journals Another approach of Morrey estimate for linear elliptic equations with partially BMO coefficients in a half space

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1429-1437
Author(s):  
Hong Tian ◽  
Shenzhou Zheng
Keyword(s):  
Half Space ◽  
Elliptic Equations ◽  
Elementary Approach ◽  
Dirichlet Problems ◽  
Spatial Variables ◽  
Morrey Estimates ◽  
Lp Estimate ◽  
Special Weight ◽  
Bmo Coefficients ◽  
Weak Derivatives

Making use of an elementary approach instead of the weighted Lp estimate with a special weight, we prove global Morrey estimates of the weak derivatives to the Dirichlet problems of linear elliptic equations with small partially BMO coefficients in a half space. Here, the leading coefficients aij(x) are assumed to be merely measurable in one variable, and have small BMO in the remaining spatial variables.

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.

Perturbation and Solvability of Initial Lp Dirichlet Problems for Parabolic Equations over Non-cylindrical Domains

2014 ◽  
Vol 66 (2) ◽  
pp. 429-452 ◽  
Author(s):  
Jorge Rivera-Noriega
Keyword(s):  
Dirichlet Problem ◽  
Parabolic Equations ◽  
Elliptic Equations ◽  
Carleson Measure ◽  
Divergence Form ◽  
Second Order ◽  
Linear Operators ◽  
Dirichlet Problems ◽  
Small Perturbations ◽  
Cylindrical Domains

AbstractFor parabolic linear operators L of second order in divergence form, we prove that the solvability of initial Lp Dirichlet problems for the whole range 1 < p < ∞ is preserved under appropriate small perturbations of the coefficients of the operators involved. We also prove that if the coefficients of L satisfy a suitable controlled oscillation in the form of Carleson measure conditions, then for certain values of p > 1, the initial Lp Dirichlet problem associated with Lu = 0 over non-cylindrical domains is solvable. The results are adequate adaptations of the corresponding results for elliptic equations.

scholarly journals The Generalized Hölder and Morrey-Campanato Dirichlet Problems for Elliptic Systems in the Upper Half-Space

2019 ◽  
Vol 53 (3) ◽  
pp. 947-976
Author(s):  
Juan José Marín ◽  
José María Martell ◽  
Marius Mitrea
Keyword(s):  
Half Space ◽  
Elliptic Systems ◽  
Dirichlet Problems

Symmetry of solutions to optimization problems related to partial differential equations

2006 ◽  
Vol 136 (5) ◽  
pp. 921-934 ◽  
Author(s):  
Fabrizio Cuccu ◽  
Giovanni Porru
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Elliptic Equations ◽  
Optimization Problems ◽  
Existence Results ◽  
Dirichlet Problems ◽  
Partial Differential ◽  
Moving Plane Method ◽  
Plane Method ◽  
Moving Plane

We investigate maxima and minima of some functionals associated with solutions to Dirichlet problems for elliptic equations. We prove existence results and, under suitable restrictions on the data, we show that any maximal configuration satisfies a special system of two equations. Next, we use the moving-plane method to find symmetry results for solutions of a system. We apply these results in our discussion of symmetry for the maximal configurations of the previous problem.

Stable and Finite Morse Index Solutions for Dirichlet Problems with Small Diffusion in a Degenerate Case and Problems with Infinite Boundary Values

2009 ◽  
Vol 9 (4) ◽  
Author(s):  
E.N. Dancer
Keyword(s):  
Elliptic Equations ◽  
Morse Index ◽  
Nonlinear Elliptic Equations ◽  
Degenerate Case ◽  
Boundary Values ◽  
Dirichlet Problems ◽  
Small Diffusion ◽  
Weakly Nonlinear ◽  
Nonlinear Elliptic

AbstractWe consider weakly nonlinear elliptic equations with small diffusion in the case where the nonlinearity has a non-nodal zero. We show that there is an unexpected connection with problems with infinite boundary values.

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