Advances in Differential Equations

Degenerate parabolic PDEs with discontinuities and generalized evolutions of surfaces

Hitoshi Ishii

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Abstract

We establish comparison theorems for solutions of degenerate parabolic partial differential equations with discontinuities (or singularities). The results are used to define the generalized evolutions of sets generated by geometric partial differential equations with discontinuities. These results generalize recent results obtained by Ohnuma-Sato ([13]) and Gurtin-Soner-Souganidis ([11]).

Article information

Source
Adv. Differential Equations, Volume 1, Number 1 (1996), 51-72.

Dates
First available in Project Euclid: 25 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366896314

Mathematical Reviews number (MathSciNet)
MR1357954

Zentralblatt MATH identifier
0841.35057

Subjects
Primary: 35K65: Degenerate parabolic equations
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]

Citation

Ishii, Hitoshi. Degenerate parabolic PDEs with discontinuities and generalized evolutions of surfaces. Adv. Differential Equations 1 (1996), no. 1, 51--72. https://projecteuclid.org/euclid.ade/1366896314


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