3 problems

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Non-uniqueness conjecture for energy minimisers in the Dirichlet problem
Let $B$ be the domain, let $f$ be prescribed Jacobian data, and consider the Dirichlet problem of minimising the relevant energy among maps with Jacobian $f$ and the prescribed bou…
Conjectureopencalculus-of-variations energy-minimisation jacobian-equationsarXiv posted 2 days ago
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Checkerboard Conjecture for energy minimisation on toric grids
Let a $d$ -dimensional toric grid have side lengths $n_1,\ldots,n_d$ , total size $n=n_1\cdots n_d$ , and Lee distance given by shortest-path distance in the grid graph. Assume that a…
Conjectureopendiscrete-geometry energy-minimisation toric-gridsarXiv posted 2 days ago
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Higher-dimensional extension of the one-dimensional copolymer-homopolymer energy lower bound
Higher-dimensional lower-bound conjecture. The same lower bound should hold in ${{\mathbb{R}}}^N$ , without making any a priori assumption on the morphology:
Conjectureopencalculus-of-variations copolymers energy-minimisationarXiv posted 2 days ago

Non-uniqueness conjecture for energy minimisers in the Dirichlet problem