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math.AP2026
A unified approach to the divergence equation and related functional inequalities
Filippo Gazzola, Hans-Christoph Grunau, Gianmarco Sperone
The huge amount of literature about the divergence equation in bounded Lipschitz domains of () is fairly disconnected and even apparently simple problems remain unsol…
math.AP2026
Regular Curves, Singular Graphs: Cantor Parts and the Relaxed Willmore Energy
Hans-Christoph Grunau, Boris Gulyak
One might expect that finite relaxed elastic energy rules out diffuse singularities in the derivative, leaving only absolutely continuous and jump parts. This is suggested by the r…
math.AP2026
Global minimizers for a two-sided biharmonic Alt-Caffarelli problem
Hans-Christoph Grunau, Marius Müller
We study global minimizers of biharmonic analogues of the Alt-Caffarelli functional. It turns out that half-space solutions are global minimizers for the two-sided Alt-Caffarelli f…