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Geometrical Properties of Fully Nonlinear Equations and an Application to Singularities

✍ Scribed by M. Badiale

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
648 KB
Volume
112
Category
Article
ISSN
0022-0396

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✦ Synopsis

In this paper several results on geometrical properties of viscosity solutions of fully nonlinear equations are presented. In particular I prove symmetry and monotonicity for solutions of fully nonlinear second order equations defined in finite cylinders, and asymptotic symmetry for solutions of fully nonlinear second order equations defined in exterior domains. Also I utilize such geometrical ideas to study the asymptotic behavior of singular viscosity solutions of first order Hamilton-Jacobi equations. c. 1994 Academic Press. Inc.

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## Abstract This paper deals with the initial and boundary value problem for a singular nonlinear parabolic equation. The existence of solutions is established by parabolic regularization. Some properties of solutions, for instance localization and large time behaviour are also discussed. Copyright