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dc.contributor.advisorMassaneda Clares, Francesc Xavier-
dc.contributor.authorIbarra García, Nerea-
dc.descriptionTreballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Francesc Xavier Massaneda Claresca
dc.description.abstract[en] In this memoir we prove a weak version in $\mathbb{R}^2$ of Kakutani's theorem which gives a solution to the Dirichlet problem. The Dirichlet problem is a classical problem in partial differential equations with many applications in various fields. Given a bounded domain $D \subset$ $\mathbb{R}^d$ and a function $f$ continuous at $\partial D$, the Dirichlet problem consists in finding an harmonic function $u$ on $D$, which matches the values of $f$ on the boundary. It is known that for very general domains the solution exists and is unique. The solution given by Kakutani in 1944 is based in the use of probabilistic methods, specifically in the properties of Brownian motion, which will play an important role throughout this
dc.format.extent49 p.-
dc.relation.isbasedonTreballs Finals de Grau (TFG) - Matemàtiques-
dc.rightscc-by-nc-nd (c) Nerea Ibarra García, 2022-
dc.subject.classificationProblema de Dirichletca
dc.subject.classificationTreballs de fi de grau-
dc.subject.classificationProblemes de contornca
dc.subject.classificationMoviment browniàca
dc.subject.classificationAnàlisi harmònicaca
dc.subject.otherDirichlet problemen
dc.subject.otherBachelor's theses-
dc.subject.otherBoundary value problemsen
dc.subject.otherBrownian movementsen
dc.subject.otherHarmonic analysisen
dc.titleThe Dirichlet problem and Kakutani’s theoremca
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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