Department of Mathematics and Systems Analysis

Research

Seminar on analysis and geometry

Talks

  • 28.2. 10:15  Timo Takala: Preserving Besov energy in sphericalization and flattening – M3 (M234)
  • 6.3. 10:15  Wontae Kim: Hölder regularity of the parabolic double phase equation – M3 (M234)
  • 13.3. 10:15  Aapo Laukkarinen: Convex body domination and its applications to matrix-weighted norm inequalities – M3 (M234)
  • 20.3. 10:15  Jonas Tölle: Nonlinear (stochastic) PDEs with singular diffusivity – M3 (M234)

    In this talk, we shall discuss properties of solutions to parabolic deterministic (and stochastic) partial differential equations with singular nonlinear divergence-type diffusivity with zero Dirichlet boundary conditions on a bounded Euclidean domain. As these kinds of equations usually lack good coercivity estimates in higher spatial dimensions, we choose to address the general well-posedness question by variational weak energy methods. Examples include the (stochastic) singular $p$-Laplace equation, the multi-valued (stochastic) total variation flow and the (stochastic) curve shortening flow. We shall present improved pathwise regularity results and decay estimates for a general class of singular divergence-type PDEs. We shall also address the stochastic case, where the equation is perturbed by additive Gaussian noise. Based on joint works with Benjamin Gess (Leipzig and Bielefeld), Wei Liu (Xuzhou), Florian Seib (Berlin), and Wilhelm Stannat (Berlin).

  • 10.4. 10:15  Lauri Särkiö: TBA – M3 (M234)
  • 17.4. 10:15  Kim Myyryläinen: TBA – M3 (M234)
  • 24.4. 10:15  Anna-Mariya Otsetova: Axisymmetric capillary water waves with vorticity and swirl connecting to static unduloid configurations – M3 (M234)

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