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Daily Overview |
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Pl 4: Plenary Lecture Location: Audimax A600 Session Chair: Franz Gmeineder | |
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Nonuniform Ellipticity and Nonlinear Potentials University of Parma
The representation formula for the Poisson equation gives an explicit expression of solutions in terms of the data, yielding zeroth- and first-order pointwise bounds via convolution with suitable Riesz potentials. Their mapping properties allow for a sharp regularity transfer from data to solutions, so that nonlinear PDEs can be treated, up to the C^{1}-level as they were linear. I will then discuss a novel potential-theoretic approach to the (ir)regularity of solutions to certain nonuniformly elliptic PDEs arising in geometric and physical models.
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