The De Giorgi conjecture on elliptic regularization
Ulisse Stefanelli
TL;DR
This paper proves De Giorgi's conjecture regarding the elliptic regularization of semilinear wave equations in finite time, advancing understanding of their regularity properties.
Contribution
It provides a proof of De Giorgi's conjecture on elliptic regularization for semilinear wave equations in finite time.
Findings
Confirmed the conjecture for finite-time cases
Established new regularity results for elliptic regularization
Enhanced theoretical understanding of wave equations
Abstract
We prove a conjecture by De Giorgi on the elliptic regularization of semilinear wave equations in the finite-time case.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Stability and Controllability of Differential Equations · Advanced Mathematical Modeling in Engineering