scholarly journals The free-boundary Brakke flow

2020 ◽  
Vol 2020 (758) ◽  
pp. 95-137 ◽  
Author(s):  
Nick Edelen
Keyword(s):  
Free Boundary ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Monotonicity Formula ◽  
Local Regularity ◽  
Regularity Theorem ◽  
Elliptic Regularization ◽  
Barrier Surface ◽  
Boundary Mean Curvature

AbstractWe develop the notion of Brakke flow with free-boundary in a barrier surface. Unlike the classical free-boundary mean curvature flow, the free-boundary Brakke flow must “pop” upon tangential contact with the barrier. We prove a compactness theorem for free-boundary Brakke flows, define a Gaussian monotonicity formula valid at all points, and use this to adapt the local regularity theorem of White [23] to the free-boundary setting. Using Ilmanen’s elliptic regularization procedure [10], we prove existence of free-boundary Brakke flows.

scholarly journals Construction of inertial manifolds by elliptic regularization

1991 ◽  
Vol 89 (2) ◽  
pp. 355-387 ◽  
Author(s):  
Eugene Fabes ◽  
Mitchell Luskin ◽  
George R Sell
Keyword(s):  
Inertial Manifolds ◽  
Elliptic Regularization

Quasilinear Equations via Elliptic Regularization Method

2013 ◽  
Vol 13 (2) ◽  
Author(s):  
Jia-Quan Liu ◽  
Xiang-Qing Liu ◽  
Zhi-Qiang Wang
Keyword(s):  
Elliptic Equations ◽  
Regularization Method ◽  
Quasilinear Elliptic Equations ◽  
Quasilinear Equations ◽  
Elliptic Regularization ◽  
Nodal Property ◽  
Quasilinear Problems ◽  
Sign Changing Solutions ◽  
Quasilinear Elliptic

AbstractIn this paper we study a class of quasilinear problems, in particular we deal with multiple sign-changing solutions of quasilinear elliptic equations. We further develop an approach used in our earlier work by exploring elliptic regularization. The method works well in studying multiplicity and nodal property of solutions.

scholarly journals THE DE GIORGI CONJECTURE ON ELLIPTIC REGULARIZATION

2011 ◽  
Vol 21 (06) ◽  
pp. 1377-1394 ◽  
Author(s):  
ULISSE STEFANELLI
Keyword(s):  
Finite Time ◽  
Wave Equations ◽  
Semilinear Wave Equations ◽  
Elliptic Regularization ◽  
De Giorgi Conjecture

We prove a conjecture by De Giorgi on the elliptic regularization of semilinear wave equations in the finite-time case.

Elliptic regularization for the semi-linear telegraph system

2010 ◽  
Vol 72 (6) ◽  
pp. 3049-3061 ◽  
Author(s):  
N.C. Apreutesei ◽  
B. Djafari Rouhani
Keyword(s):  
Elliptic Regularization
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