The Harnack inequality for second-order elliptic equations with divergence-free drifts     Harnack inequality  second-order elliptic equations  divergence-free drifts       font style='font-size:12px;'> 2015/7/14

We consider an elliptic equation with a divergence-free drift b. We prove that an inequality of Harnack type holds under the assumption b ∈ Ln/2+δ ∩ L2 where δ > 0. As an application we provide a one ...

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On non-local reflection for elliptic equations of the second order in R^2 (the Dirichlet condition)     elliptic equations  the second order in R^2 (the Dirichlet condition)       font style='font-size:12px;'> 2010/12/1

Point-to-point re ection holding for harmonic functions subject to the Dirichlet or Neumann conditions on an analytic curve in the plane almost always fails for solutions to more general elliptic equ...

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Hôlder continuity of solutions of second-order non-linear elliptic integro-differential equations      H¨older regularity  integro-differential equations  L´  evy operators  general non-local operators       font style='font-size:12px;'> 2010/11/29

This paper is concerned with H¨older regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we ass...

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On the Boundary Behaviour, Including Second Order Effects, of Solutions to Singular Elliptic Problems     elliptic problems    singular equations    boundary behaviour       font style='font-size:12px;'> 2007/12/11

For $\gamma\ge 1$ we consider the solution $u=u(x)$ of the Dirichlet boundary value problem $\Delta u+u^{-\gamma}=0$ in $\Omega$, $u=0$ on $\partial\Omega$. For $\gamma=1$ we find the estimate $$u(x)=...

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