# Mathematicians Dissertations

$$v\bigm|_=u\bigm|_ \qquad \implies \qquad \|\nabla u\|_\leq \|\nabla v\|_.$$! is absolutely minimizing if and only if it is the solution of the infinity Laplacian, which is the (highly degenerate) Euler-Lagrange equation for the prototypical problem in the calculus of variations in ! Recommended modules: Functional Analysis, Partial Differential Equations References: !

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\begin \tag* P (E^S) \leq P(E) \quad \text E \subset \mathbb^n.

, and (see, for instance, Theorem 14.4 in [3]) is satisfied: !