5 papers
ELADO: Elliptic PDE Assessment Datasets for Operator Learning
Frank Ehebrecht, Toni Scharle, Martin Atzmueller
We introduce ELADO (Elliptic PDE Assessment Datasets for Operator Learning), a systematic benchmark suite constructed to show and quantify failure modes of neural operator architec…
The De Giorgi method for local and nonlocal systems
Linus Behn, Lars Diening, Simon Nowak +1
We extend the De Giorgi iteration technique to the vectorial setting. For this we replace the usual scalar truncation operator by a vectorial shortening operator. As an application…
Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations
Lars Diening, Toni Scharle, Endre Süli
We develop a discrete counterpart of the De Giorgi-Nash-Moser theory, which provides uniform Hölder-norm bounds on continuous piecewise affine finite element approximations of seco…
The local boundedness of gradients of weak solutions to elliptic and parabolic phi-Laplacian systems
Toni Scharle
In this thesis, a unified approach to prove the boundedness of gradients of solutions to degenerate and singular elliptic and parabolic phi-Laplacian systems is presented. At first…
Regularity for parabolic systems of Uhlenbeck type with Orlicz growth
Lars Diening, Toni Scharle, Sebastian Schwarzacher
We study the local regularity of -caloric functions or more generally of -caloric functions. In particular, we study local solutions of non-linear parabolic systems with homo…