Hessian Estimates for Nondivergence Parabolic and Elliptic Equations with Partially BMO Coefficients

2019 ◽  
Vol 75 (1) ◽  
Author(s):  
Junjie Zhang ◽  
Shenzhou Zheng
Keyword(s):  
Elliptic Equations ◽  
Hessian Estimates ◽  
Bmo Coefficients

Weighted Orlicz regularity estimates for fully nonlinear elliptic equations with asymptotic convexity

2019 ◽  
Vol 21 (04) ◽  
pp. 1850024 ◽  
Author(s):  
Mikyoung Lee
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Operator ◽  
Orlicz Spaces ◽  
Nonlinear Elliptic Equations ◽  
Fully Nonlinear Elliptic Equations ◽  
Fully Nonlinear ◽  
Nonlinear Elliptic ◽  
Regularity Estimates ◽  
Hessian Estimates ◽  
Asymptotic Convexity

We prove interior Hessian estimates in the setting of weighted Orlicz spaces for viscosity solutions of fully nonlinear, uniformly elliptic equations [Formula: see text] under asymptotic assumptions on the nonlinear operator [Formula: see text] The results are further extended to fully nonlinear, asymptotically elliptic equations.

Global regularity estimates for non-divergence elliptic equations on weighted variable Lebesgue spaces

2020 ◽  
pp. 2050014
Author(s):  
The Quan Bui ◽  
The Anh Bui ◽  
Xuan Thinh Duong
Keyword(s):  
Elliptic Equations ◽  
Global Regularity ◽  
Order Elliptic Equation ◽  
Lebesgue Spaces ◽  
Variable Lebesgue Spaces ◽  
Regularity Estimates ◽  
Sparse Operators ◽  
Second Order Elliptic Equation ◽  
Bmo Coefficients ◽  
Weighted Variable

This paper is to prove global regularity estimates for solutions to the second-order elliptic equation in non-divergence form with BMO coefficients in a [Formula: see text] domain on weighted variable exponent Lebesgue spaces. Our approach is based on the representations for the solutions to the non-divergence elliptic equations and the domination technique by sparse operators in harmonic analysis.

scholarly journals Global W1,p(·) estimate for renormalized solutions of quasilinear equations with measure data on Reifenberg domains

2018 ◽  
Vol 7 (4) ◽  
pp. 517-533 ◽  
Author(s):  
The Anh Bui
Keyword(s):  
Elliptic Equations ◽  
Variable Exponent ◽  
Quasilinear Elliptic Equations ◽  
Measure Data ◽  
Renormalized Solutions ◽  
Lebesgue Spaces ◽  
Quasilinear Equations ◽  
Bmo Coefficients ◽  
Reifenberg Flat ◽  
Quasilinear Elliptic

AbstractIn this paper, we prove the gradient estimate for renormalized solutions to quasilinear elliptic equations with measure data on variable exponent Lebesgue spaces with BMO coefficients in a Reifenberg flat domain.

On weighted W2,p estimates for elliptic equations with BMO coefficients in nondivergence form

2015 ◽  
Vol 26 (01) ◽  
pp. 1550001 ◽  
Author(s):  
Sun-Sig Byun ◽  
Mikyoung Lee
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Elliptic Equations ◽  
Nondivergence Form ◽  
Muckenhoupt Class ◽  
The Matrix ◽  
Bmo Coefficients

We establish global weighted W2,p, 2 < p < ∞, estimates for the solution to the Dirichlet problem for an elliptic equation in nondivergence form with BMO coefficients in a C1,1 domain under the assumption that the matrix of the coefficients has a small BMO semi-norm while the associated weight belongs to a Muckenhoupt class. These conditions are weaker than those reported in the literature.

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.

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