From energy bounds to dimensional estimates in a branched transport model for type-I superconductors
Guido De Philippis; Michael Goldman; Berardo Ruffini · 2023 · arXiv
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Abstract (excerpt)
We consider a branched transport type problem which describes the magnetic flux through type-I superconductors in a regime of very weak applied fields. At the boundary of the sample, deviation of the magnetization from being uniform is penalized through a negative Sobolev norm. It was conjectured by S. Conti, F. Otto and S. Serfaty that as a result, the trace of the magnetization on the boundary should be a measure of Hausdorff dimension $8/5$. We prove that this conjecture is equivalent to the proof of local energy bounds with an optimal exponent. We then obtain local bounds which are however
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Metadata source: arXiv