Georg S. Weiss

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math.AP2024

A singular perturbation approach to the Dirichlet-area minimisation problem

Anthony Salib, Georg S. Weiss

We study both one and two-phase minimisers of the Dirichlet-area energy $E (v) = \int_{B_{1}} ∣\nabla v ∣^{2} + P er ({v > 0}, B_{1}) .$ In the two-phase case, we show that the energ…

math.AP2024

Classification of global solutions to the obstacle problem in the plane

Anthony Salib, Georg Weiss

Global solutions to the obstacle problem were first completely classified in two dimensions by Sakai using complex analysis techniques. Although the complex analysis approach produ…