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.
|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|
|Keywords:||Non-linear potential theory, p(x)-Laplace equation, Removability, Sub-Riemannian Geometry, Viscosity solutions|
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