### Department of Mathematics and Systems Analysis

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* Dates within the next 7 days are marked by a star.

Christoph Scheven (University of Duisburg-Essen)**The obstacle problem for the porous medium equation: Existence and regularity results***** Today * ** Wednesday 26 September 2018, 12:15, M3 (M234)

In the talk we will present some results on existence and regularity of solutions to the obstacle problem associated to the porous medium equation. In particular, we will report on recent results concerning the higher integrability of the spatial gradient of solutions.

Seminar on analysis and geometry

Juha-Pekka Puska**Optimizing heating patterns in thermal tomography***** ** Thursday 27 September 2018, 14:15, M2 (M233)

Augusto Gerolin (University of Jyväskylä)**Kantorovich Duality in Optimal Transport Theory with repulsive costs**

Wednesday 03 October 2018, 12:15, M3 (M234)

Seminar on Analysis and Geometry

Arttu Karppinen (University of Turku)**Higher integrability of the gradient of a minimizer with generalized Orlicz growth**

Wednesday 10 October 2018, 12:15, M3 (M234)

In this talk we prove global higher integrability of a minimizer of an obstacle problem with generalized Orlicz growth conditions. This recovers the similiar results of the special cases such as polynomial, variable exponent and double phase growth.

Seminar on Analysis and Geometry

Vasiliki Evdoridou (The Open University, UK)**TBA**

Wednesday 17 October 2018, 12:15, M3 (M234)

Seminar on analysis and geometry

Karl Brustad (NTNU, Trondheim)**TBA**

Wednesday 31 October 2018, 12:15, M3 (M234)

Seminar on analysis and geometry

Vito Buffa (University of Ferrara)**BV Functions in Metric Measure Spaces: Traces and Integration by Parts Formulæ**

Wednesday 07 November 2018, 12:15, M3 (M234)

We adapt the tools from the differential structure developed by N. Gigli in order to give a definition of BV functions on RCD(K,\infty) spaces via suitable vector fields and then establish an extended Gauss-Green formula on a class of "regular" domains, which features the "normal trace" of vector fields with finite divergence measure. Then, we pass to the more classical context of a doubling metric measure space supporting a Poincaré inequality, where we reformulate the theory of "rough traces" of BV functions (after V. Maz'ya) in comparison with the Lebesgue-points characterization, and discuss the conditions under which the respective notions of trace coincide. Based on a joint work with M. Miranda Jr.

Seminar on analysis and geometry

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