Dissertation/Thesis Abstract

On the p(x)-Laplace Equation in Carnot Groups
by Freeman, Robert D., Ph.D., University of South Florida, 2020, 88; 27743202
Abstract (Summary)

In this thesis, we examine the p(x)-Laplace equation in the context of Carnot groups. The p(x)-Laplace

equation is the prototype equation for a class of nonlinear elliptic partial differential equations having so-called

nonstandard growth conditions. An important and useful tool in studying these types of equations is

viscosity theory. We prove a p()-Poincar´e-type inequality and use it to prove the equivalence of potential

theoretic weak solutions and viscosity solutions to the p(x)-Laplace equation. We exploit this equivalence

to prove a Rad´o-type removability result for solutions to the p-Laplace equation in the Heisenberg group.

Then we extend this result to the p(x)-Laplace equation in the Heisenberg group.

Indexing (document details)
Advisor: Bieske, Thomas
Commitee: Kouchekian, Sherwin, Teodorescu, Razvan, You, Yuncheng, Kamp, Bradley
School: University of South Florida
Department: Mathematics and Statistics
School Location: United States -- Florida
Source: DAI-B 81/10(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Non-linear potential theory, p(x)-Laplace equation, Removability, Sub-Riemannian Geometry, Viscosity solutions
Publication Number: 27743202
ISBN: 9798607350734
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