Green's Function for Nondivergence Elliptic Operators in Two Dimensions

DOI10.1137/20M1323618zbMath1479.35257arXiv2003.11185OpenAlexW3013710731MaRDI QIDQ4958014

Seick Kim, Hongjie Dong

Publication date: 6 September 2021

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.11185

zbMATH Keywords

Green's functionbounded mean oscillationDini mean oscillation

Mathematics Subject Classification ID

Second-order elliptic equations (35J15) Green's functions for elliptic equations (35J08)

Related Items (6)

Note on Green’s functions of non-divergence elliptic operators with continuous coefficients ⋮ Green function estimates for second order elliptic operators in non-divergence form with Dini continuous coefficients ⋮ Uniform estimates of resolvents in homogenization theory of elliptic systems ⋮ Learning elliptic partial differential equations with randomized linear algebra ⋮ Homogenization theory of elliptic system with lower order terms for dimension two ⋮ Estimates for Green's Functions of Elliptic Equations in Non-Divergence Form with Continuous Coefficients

Cites Work

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• Some remarks on the \(L^p\) regularity of second derivatives of solutions to non-divergence elliptic equations and the Dini condition
• Alternative proof for the existence of Green's function
• On \(C^1\), \(C^2\), and weak type-\((1,1)\) estimates for linear elliptic operators. II
• On the \(L_p\)-solvability of higher-order parabolic and elliptic systems with BMO coefficients
• Positive solutions of elliptic equations in nondivergence form and their adjoints
• Regularized distance and its applications
• Existence and regularity of very weak solutions of the stationary Navier-Stokes equations
• The \(L^ p\)-integrability of Green's functions and fundamental solutions for elliptic and parabolic equations
• The Green function for uniformly elliptic equations
• Principle de Harnack à la frontière et théorème de Fatou pour un opérateur elliptique dans un domaine lipschitzien
• Stationary solutions to the Navier-Stokes equations in dimension four
• Continuity of solutions of uniformly elliptic equations in \(\mathbb{R}^ 2\)
• Elliptic partial differential equations of second order
• Green's function for second order elliptic equations in non-divergence form
• The Green function estimates for strongly elliptic systems of second order
• On the adjoint of an elliptic linear differential operator and its potential theory
• The Green Function for Elliptic Systems in Two Dimensions
• On C¹, C², and weak type-(1,1) estimates for linear elliptic operators
• On the fundamental solution of an elliptic equation in nondivergence form
• $H^{p}$ spaces over open subsets of $R^{n}$
• Green’s matrices of second order elliptic systems with measurable coefficients in two dimensional domains
• Equivalence of the Green's Functions for Diffusion Operators in R n : A Counterexample
• On One-Point Weak Uniqueness for Elliptic Equations
• The dual of Hardy spaces on a bounded domain in ℝ n
• Bounds for the fundamental solutions of elliptic and parabolic equations
• On the oblique derivative problem for second order elliptic equations
• The Green function for the mixed problem for the linear Stokes system in domains in the plane

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