113 research outputs found
A regularity result for the inhomogeneous normalized infinity Laplacian
We prove that the unique solution to the Dirichlet problem with constant
source term for the inhomogeneous normalized infinity Laplacian on a convex
domain of is of class . The result is obtained by showing
as an intermediate step the power-concavity (of exponent ) of the
solution.Comment: 11 pages. arXiv admin note: text overlap with arXiv:1410.611
Characterization of stadium-like domains via boundary value problems for the infinity Laplacian
We give a complete characterization, as "stadium-like domains", of convex
subsets of where a solution exists to Serrin-type
overdetermined boundary value problems in which the operator is either the
infinity Laplacian or its normalized version. In case of the not-normalized
operator, our results extend those obtained in a previous work, where the
problem was solved under some geometrical restrictions on . In case of
the normalized operator, we also show that stadium-like domains are precisely
the unique convex sets in where the solution to a Dirichlet
problem is of class .Comment: 21 page
Anzellotti's pairing theory and the Gauss--Green theorem
In this paper we obtain a very general Gauss-Green formula for weakly
differentiable functions and sets of finite perimeter. This result is obtained
by revisiting Anzellotti's pairing theory and by characterizing the measure
pairing when is a bounded divergence
measure vector field and is a bounded function of bounded variation.Comment: 27 page
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