Seuri Basilio Kuosmanen: Symmetry in a free boundary problem
Master Thesis
Tid: Ti 2023-04-18 kl 10.15 - 11.00
Plats: KTH, 3418
Respondent: Seuri Basilio Kuosmanen
Handledare: Henrik Shahgholian
Abstract:
We consider a variational formulation of a Bernoulli-type free boundary problem for the Laplacian operator with discontinuous boundary data. We show the existence of a weak solution to the problem. Moreover, we show that the solution has symmetry properties inherited by symmetric data. These results are achieved through the use of comparison arguments, the celebrated method of moving planes, and several elaborated techniques from existing literature.