Stacjonarne zagadnienie przepływu ciepła na niżej wymiarowych zbiorach prostowalnych w $R^N$

Speaker(s)

Anna Zatorska-Goldstein

Affiliation

Uniwersytet Warszawski (MIM)

Date

Oct. 4, 2018, 12:30 p.m.

Room

room 5070

Seminar

Seminar of Mathematical Physics Equations Group

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I will discuss an elementary linear elliptic equation on a lower dimensional rectifiable structure in $R^N$ with Neumann boundary data. The set may be described by means of a finite Borel measure µ supported on it. This allows us to reformulate the equation and the boundary condition and to establish existence and uniqueness of a weak solution via a variational method. The setting requires an appropriate definition of a Sobolev-type space dependent on the measure µ and an appropriate Poincaré-type inequality. I will present examples of structures that are not manifolds and which do not support a global Poincaré inequality, yet which are admissible for our setting.

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