14:00 - 16:00
STEM Centre 3.1
Dr Murat Akman
Lectures, talks and seminars
Mathematical Sciences Departmental Seminar
Mathematical Sciences, Department of
Andrew Harrison email@example.com
This talk has been cancelled.
These Departmental Seminars are for everyone interested in Maths. We encourage anyone interested in the subject in general, or in the particular subject of the seminar, to come along. It's a great opportunity to meet people in the Maths Department and join in with our community.
Refreshments are shared in the Department (STEM 5.1) after every seminar.
The classical Minkowski problem consists in finding a convex polyhedron from data consisting of normals to their faces and their surface areas. In the smooth case, the corresponding problem for convex bodies is to find the convex body given the Gauss curvature of its boundary, as a function of the unit normal. The proof consists of three parts: existence, uniqueness and regularity.
In this talk, we study a Minkowski problem for certain measure associated with a compact convex set E with nonempty interior and its A-harmonic capacitary function in the complement of E. Here A-harmonic PDE is a non-linear elliptic PDE whose structure is modelled on the p-Laplace equation.
If \mu_E denotes this measure, then the Minkowski problem we consider in this setting is that; for a given finite Borel measure \mu on S^(n-1), find necessary and sufficient conditions for which there exists E as above with \mu_E =\mu. We will discuss the existence, uniqueness, and regularity of this problem in this setting.
The talk will be related to the following papers:
Dr Murat Akman is a Lecturer in the Department of Mathematical Sciences, University of Essex.