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March/April 2013 Limiting observations for planar free-boundaries governed by isotropic-anisotropic singular diffusions, upper bounds for the limits
Ken Shirakawa
Adv. Differential Equations 18(3/4): 351-383 (March/April 2013).

Abstract

In this paper, variational inclusions of Euler--Lagrange types, governed by two-dimensional isotropic-anisotropic singular diffusions, are considered. On that basis, we focus on the geometric structures of free boundaries where anisotropic conditions tend to isotropic. In this light, a limit-set of special piecewise-constant solutions will be presented. The objective in this paper is to give some observations on the upper bounds of the limit set with geometric characterizations. As a consequence, it will be shown that the isotropic free boundaries, as in the limit set, consist of a finite number of $ C^{1,1} $-Jordan curves, and these have certain geometric connections with the approaching anisotropic situations. Observations for the lower bounds will be studied in the sequel to this paper.

Citation

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Ken Shirakawa. "Limiting observations for planar free-boundaries governed by isotropic-anisotropic singular diffusions, upper bounds for the limits." Adv. Differential Equations 18 (3/4) 351 - 383, March/April 2013.

Information

Published: March/April 2013
First available in Project Euclid: 5 February 2013

zbMATH: 1259.35227
MathSciNet: MR3060199

Subjects:
Primary: 14H50 , 35J75 , 35R35

Rights: Copyright © 2013 Khayyam Publishing, Inc.

JOURNAL ARTICLE
33 PAGES

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Vol.18 • No. 3/4 • March/April 2013
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