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Department of Mathematics and Systems Analysis
Lectures, seminars and dissertations in mathematics
* Dates within the next 7 days are marked by a star.
Harri Varpanen
Wolffs conjecture for p-harmonic functions in the plane
* Today * Wednesday 22 May 2013, 12:15, room U322
In 1984 Tom Wolff conjectured the existence of a bounded p-harmonic function that fails Fatous radial limit theorem in the unit disc. I will survey the conjecture in some detail. No previous familiarity with p-harmonic functions is assumed.
Analysis and geometry seminar/ Kinnunen, Peltonen
Prof. Jose Miguel Urbano
An introduction to the ∞-Laplacian
* Thursday 23 May 2013, 10:15, Room U322
The mini-course is an introduction to the study of the ∞-Laplace equation. We start with an historical tour of the theory, from the pioneering work of Aronsson to recent developments on the regularity of solutions. The heart of the course is a rigorous and detailed analysis of the equivalence between being absolutely minimizing Lipschitz, satisfying comparison with cones and solving the the ∞-Laplace equation in the viscosity sense. An easy proof of the celebrated theorem of Jensen on the uniqueness of infinity harmonic functions, due to Armstrong and Smart, and a digression on the state of the art concerning their regularity conclude the set of lectures.
Prof. Jose Miguel Urbano
An introduction to the ∞-Laplacian
* Friday 24 May 2013, 10:15, Room U322
The mini-course is an introduction to the study of the ∞-Laplace equation. We start with an historical tour of the theory, from the pioneering work of Aronsson to recent developments on the regularity of solutions. The heart of the course is a rigorous and detailed analysis of the equivalence between being absolutely minimizing Lipschitz, satisfying comparison with cones and solving the the ∞-Laplace equation in the viscosity sense. An easy proof of the celebrated theorem of Jensen on the uniqueness of infinity harmonic functions, due to Armstrong and Smart, and a digression on the state of the art concerning their regularity conclude the set of lectures.
Hans Hartikainen (Jyväskylä)
∞-Laplacian and Tug-of-War Game
Wednesday 29 May 2013, 12:15, U322
Analysis and geometry seminar/ Kinnunen, Peltonen