G. Sakellaris

activity

20172025

most citedGreen's function for second order elliptic equations with singular lower order coefficients

23 citations · 39 across the 7 of their papers we have counts for

collaborators

8 papers

math.AP2025

Two-sided Gaussian estimates for fundamental solutions of second-order parabolic equations in non-divergence form

Seick Kim, Sungjin Lee, Georgios Sakellaris

We establish two-sided Gaussian bounds for the fundamental solution of second-order parabolic operators in non-divergence form under minimal regularity assumptions. Specifically, w…

math.AP2023★ 3 cited

The Neumann Green function and scale invariant regularity estimates for elliptic equations with Neumann data in Lipschitz domains

Seick Kim, Georgios Sakellaris

We construct the Neumann Green function and establish scale invariant regularity estimates for solutions to the Neumann problem for the elliptic operator $Lu=-{\rm div}({\bf A} \na…

math.AP2020

Scale invariant regularity estimates for second order elliptic equations with lower order coefficients in optimal spaces

Georgios Sakellaris

We show local and global scale invariant regularity estimates for subsolutions and supersolutions to the equation $- div (A \nabla u + b u) + c \nabla u + d u = - div f + g$ , assuming th…

math.AP2019

Minimizers for the thin one-phase free boundary problem

Max Engelstein, Aapo Kauranen, Martí Prats +2

We consider the "thin one-phase" free boundary problem, associated to minimizing a weighted Dirichlet energy of the function in $R_{+}^{n + 1}$ plus the area of the positivity…

math.AP2019★ 10 cited

On scale invariant bounds for Green's function for second order elliptic equations with lower order coefficients and applications

Georgios Sakellaris

We construct Green's functions for elliptic operators of the form $L u = - div (A \nabla u + b u) + c \nabla u + d u$ in domains $Ω \subseteq R^{n}$ , under the assumption $d\…

math.AP2018

Boundary value problems in Lipschitz domains for equations with lower order coefficients

Georgios Sakellaris

We use the method of layer potentials to study the $R_{2}$ Regularity problem and the $D_{2}$ Dirichlet problem for second order elliptic equations of the form $L u = 0$ , with l…

math.AP2017★ 23 cited

Green's function for second order elliptic equations with singular lower order coefficients

Seick Kim, Georgios Sakellaris

We construct Green's function for second order elliptic operators of the form $Lu = - \nabla \cdot (A \nabla u + b u) + c \cdot \nabla u + d u$ in a dom…

math.AP2017★ 3 cited

Boundary value problems in Lipschitz domains for equations with drifts

Georgios Sakellaris

In this work we establish solvability and uniqueness for the $D_{2}$ Dirichlet problem and the $R_{2}$ Regularity problem for second order elliptic operators $L=-{\rm div}(A\nabla\cdot…