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math-ph2023
From incommensurate bilayer heterostructures to Allen-Cahn: An exact thermodynamic limit
Michael Hott, Alexander B. Watson, Mitchell Luskin
We give a complete and rigorous derivation of the mechanical energy for twisted 2D bilayer heterostructures without any approximation beyond the existence of an empirical many-body…
math.FA2023
Upper bounds on homogeneous fractional Gagliardo-Nirenberg-Sobolev constants via parabolic estimates
Michael Hott
Common proofs of the Gagliardo-Nirenberg-Sobolev (GNS) do not provide explicit bounds on the involved constants, unless a sharp constant is being determined. GNS inequalities natur…