First existence and uniqueness results for quasilinear Allen-Cahn systems with non-convex gradient energy, via maximal regularity for strong solutions and minimizing movements plus higher integrability for weak solutions.
The gradient theory of phase transitions and the minimal interface criterion
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The fractional Massari functional Gamma-converges to the classical Massari functional, preserving minimizers, and yields limiting information for inhomogeneous Allen-Cahn equations together with the new notion of non-local hybrid mean curvature.
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$\Gamma$-convergence of the non-local Massari functional and applications to inhomogeneous Allen-Cahn equations
The fractional Massari functional Gamma-converges to the classical Massari functional, preserving minimizers, and yields limiting information for inhomogeneous Allen-Cahn equations together with the new notion of non-local hybrid mean curvature.