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- Title
Existence and uniqueness of viscosity solutions to the infinity Laplacian relative to a class of Grushin-type vector fields.
- Authors
BIESKE, THOMAS; FORREST, ZACHARY
- Abstract
In this paper, we pose the1-Laplace equation as a Dirichlet Problem in a class of Grushin-type spaces whose vector fields are of the form... and k is not a polynomial for indices m + 1 k n. Solutions to the1-Laplacian in the viscosity sense have been shown to exist and be unique in [3], when k is a polynomial; we extend these results by exploiting the relationship between Grushin-type and Euclidean second-order jets and utilizing estimates on the viscosity derivatives of sub-and supersolutions in order to produce a comparison principle for semicontinuous functions.
- Subjects
VISCOSITY; LAPLACIAN matrices; VECTORS (Calculus); EUCLIDEAN geometry; POLYNOMIALS
- Publication
Constructive Mathematical Analysis, 2023, Vol 6, Issue 2, p77
- ISSN
2651-2939
- Publication type
Article
- DOI
10.33205/cma.1245581