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PDE Seminar - Peter Takac

Ohio State Garden of Constants
November 19, 2024
10:20 am - 11:20 am
Math Tower (MW) 100A

Peter Takac
Institut f¨ur Mathematik, Universit¨at Rostock

Title
A p(x)-Laplacian Extension of a Convexity Result and Applications to Quasi-linear Elliptic BVPs

Abstract
The main result of this work is a new extension of the well-known inequality by Dı́az and Saa which, in our case, involves an anisotropic operator, such as the p(x)-Laplacian, ∆ p(x) u ≡ div(|∇u| p(x)−2 ∇u). Our present extension of this inequality enables us to establish several new results on the uniqueness of solutions and comparison principles for some anisotropic quasilinear elliptic equations. Our proofs take advantage of certain convexity properties of the energy functional associated with the p(x)-Laplacian.

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