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On Viscosity and Equivalent Notions of Solutions for Anisotropic Geometric Equations
Joint Authors
De Zan, Cecilia
Soravia, Pierpaolo
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-01-08
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
We prove that viscosity solutions of geometric equations in step two Carnot groups can be equivalently reformulated by restricting the set of test functions at the singular points.
These are characteristic points for the level sets of the solutions and are usually difficult to deal with.
A similar property is known in the Euclidian space, and in Carnot groups, it is based on appropriate properties of a suitable homogeneous norm.
We also use this idea to extend to Carnot groups the definition of generalised flow, and it works similarly to the Euclidian setting.
These results simplify the handling of the singularities of the equation, for instance, to study the asymptotic behaviour of singular limits of reaction diffusion equations.
We provide examples of using the simplified definition, showing, for instance, that boundaries of strictly convex subsets in the Carnot group structure become extinct in finite time when subject to the horizontal mean curvature flow even if characteristic points are present.
American Psychological Association (APA)
De Zan, Cecilia& Soravia, Pierpaolo. 2020. On Viscosity and Equivalent Notions of Solutions for Anisotropic Geometric Equations. Abstract and Applied Analysis،Vol. 2020, no. 2020, pp.1-14.
https://search.emarefa.net/detail/BIM-1119935
Modern Language Association (MLA)
De Zan, Cecilia& Soravia, Pierpaolo. On Viscosity and Equivalent Notions of Solutions for Anisotropic Geometric Equations. Abstract and Applied Analysis No. 2020 (2020), pp.1-14.
https://search.emarefa.net/detail/BIM-1119935
American Medical Association (AMA)
De Zan, Cecilia& Soravia, Pierpaolo. On Viscosity and Equivalent Notions of Solutions for Anisotropic Geometric Equations. Abstract and Applied Analysis. 2020. Vol. 2020, no. 2020, pp.1-14.
https://search.emarefa.net/detail/BIM-1119935
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1119935