Displaying similar documents to “Comparison results between minimal barriers and viscosity solutions for geometric evolutions”

Barriers for a class of geometric evolution problems

Giovanni Bellettini, Matteo Novaga (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We present some general results on minimal barriers in the sense of De Giorgi for geometric evolution problems. We also compare minimal barriers with viscosity solutions for fully nonlinear geometric problems of the form u t + F ⁢ t , x , ∇ ⁡ u , ∇ 2 ⁡ u = 0 . If F is not degenerate elliptic, it turns out that we obtain the same minimal barriers if we replace F with F + , which is defined as the smallest degenerate elliptic function above F .

Two examples of fattening for the curvature flow with a driving force

Giovanni Bellettini, Maurizio Paolini (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We provide two examples of a regular curve evolving by curvature with a forcing term, which degenerates in a set having an interior part after a finite time.

The relation between the porous medium and the eikonal equations in several space dimensions.

Pierre-Louis Lions, Panagiotis E. Souganidis, Juan Luis Vázquez (1987)

Revista Matemática Iberoamericana

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We study the relation between the porous medium equation ut = Δ(um), m > 1, and the eikonal equation vt = |Dv|2. Under quite general assumtions, we prove that the pressure and the interface of the solution of the Cauchy problem for the porous medium equation converge as m↓1 to the viscosity solution and the interface of the Cauchy problem for the eikonal equation. We also address the same...