Sharp Green function estimates for \(\Delta + \delta ^{\alpha /2}\) in \(C^{1,1}\) open sets and their applications

zbMath1257.31002arXiv0912.2765MaRDI QIDQ1928867

Panki Kim, Zoran Vondraček, Zhen-Qing Chen, Renming Song

Publication date: 4 January 2013

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.2765

zbMATH Keywords

Brownian motionMartin boundaryLévy processpseudo differential operator

Mathematics Subject Classification ID

Related Items (17)

Mixed local and nonlocal elliptic operators: regularity and maximum principles ⋮ Green function estimates for subordinate Brownian motions: Stable and beyond ⋮ Boundary Harnack principle for diffusion with jumps ⋮ Linear theory for a mixed operator with Neumann conditions ⋮ On the regularity theory for mixed local and nonlocal quasilinear elliptic equations ⋮ Existence and multiplicity results for nonlocal Lane-Emden systems ⋮ Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations ⋮ (Non)local logistic equations with Neumann conditions ⋮ Fractional nonlinear degenerate diffusion equations on bounded domains. I: Existence, uniqueness and upper bounds. ⋮ De Giorgi type results for equations with nonlocal lower-order terms ⋮ Gradient regularity in mixed local and nonlocal problems ⋮ Interior and boundary regularity results for strongly nonhomogeneous \((p, q)\)-fractional problems ⋮ Semilinear elliptic equations involving mixed local and nonlocal operators ⋮ Harnack inequality for non-local Schrödinger operators ⋮ Local versus nonlocal elliptic equations: short-long range field interactions ⋮ Global regularity results for non-homogeneous growth fractional problems ⋮ An Elliptic Boundary Value Problem with Fractional Nonlinearity

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