Shadows of infinities
Tuomo Kuusi, Peter Lindqvist, Mikko Parviainen
TL;DR
This paper investigates the behavior of unbounded supersolutions to the Evolutionary p-Laplace equation, revealing a dichotomy in their local summability properties related to their growth and integrability.
Contribution
It establishes a novel dichotomy in the local summability of supersolutions, connecting viscosity solutions with unbounded supersolutions in the context of the Evolutionary p-Laplace equation.
Findings
Supersolutions are either summable to the power p-1+n/p-0 or not to the power p-2+0.
A clear dichotomy in the local integrability properties of supersolutions is demonstrated.
Viscosity supersolutions coincide with unbounded supersolutions for the equation.
Abstract
We study unbounded "supersolutions" of the Evolutionary -Laplace equation with slow diffusion. They are the same functions as the viscosity supersolutions. A fascinating dichotomy prevails: either they are locally summable to the power or not summable to the power
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Taxonomy
TopicsNonlinear Partial Differential Equations · Geometric Analysis and Curvature Flows · Stochastic processes and statistical mechanics