Benny Avelin

Boundary estimates for certain degenerate and singular parabolic equations

We study the boundary behavior of non-negative solutions to a class of degenerate/singular parabolic equations, whose prototype is the parabolic

A comparison principle for the porous medium equation and its consequences

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Boundary behavior of solutions to the parabolic p-Laplace equation

-Laplacian. Assuming that such solutions continuously vanish on some distinguished part of the lateral part

A Carleson type inequality for fully nonlinear elliptic equations with non-Lipschitz drift term

S_T

Characterizations of interior polar sets for the degenerate p-parabolic equation

of a Lipschitz cylinder, we prove Carleson-type estimates, and deduce some consequences under additional assumptions on the equation or the domain. We then prove analogous estimates for non-negative solutions to a class of degenerate/singular parabolic equations, of porous medium type.

Nonlinear Calderón–Zygmund Theory in the Limiting Case

We prove a comparison principle for the porous medium equation in more general open sets in

Estimates for Solutions to Equations of p-Laplace type in Ahlfors regular NTA-domains

mathbb{R}^{n+1}

On time dependent domains for the degenerate p-parabolic equation: Carleson estimate and Hölder continuity

than space-time cylinders. We apply this result in two related contexts: we establish a connection between a potential theoretic notion of the obstacle problem and a notion based on a variational inequality. We also prove the basic properties of the PME capacity, in particular that there exists a capacitary extremal which gives the capacity for compact sets.

Lower semicontinuity of weak supersolutions to the porous medium equation

This paper is the second installment in a series of papers concerning the boundary behavior of solutions to the

Wolff-Potential Estimates and Doubling of Subelliptic p-harmonic measures

p