Existence of Lipschitz minimizers for the three-well problem in solid-solid phase transitions

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More precisely, we prove existence and uniqueness of the solution for this problem in two different settings: the case with degenerated enthalpy function and a fixed vectorial

For the Lipschitz coefficient case one can apply a monotonicity formula to prove the C 1,1 -regularity of the solution and that the free boundary is, near the so-called

In Section 3, we derive a precise blow-up scenario and present a global existence result of strong solutions to Equation (1.1).. In Section 4, we prove that Equation (1.1) has

Theorem 2. The following theorem makes a relation among the H¨older-regularity of the coefficients of the principal part, the bound on its derivatives and the order of the Gevrey

In [6], Pucci cites a necessary and sufficient condition for the existence of a solution to the Cauchy problem for the Laplace equation for a rec- tangle in a

The first non existence result for global minimizers of the Ginzburg-Landau energy with prescribed degrees p 6 = q and pq > 0 was obtained by Mironescu in [Mir13] following the

The H 2 -regularity of variational solutions to a two-dimensional transmission problem with geometric constraint is investigated, in particular when part of the interface becomes