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Seuri Basilio Kuosmanen: Symmetry in a free boundary problem

Master Thesis

Time: Tue 2023-04-18 10.15 - 11.00

Location: KTH, 3418

Respondent: Seuri Basilio Kuosmanen

Supervisor: Henrik Shahgholian

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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.