2 citations · 3 across the 7 of their papers we have counts for
9 papers
A Uniqueness Theorem for Mean Value Sets for Elliptic Divergence Form Operators
Niles Armstrong, Ivan Blank
We give background which shows the connection between the mean value theorem and the obstacle problem, and then we prove that a set is a mean value set for an elliptic operator of…
Nondegenerate Motion of Singular Points in Obstacle Problems with Varying Data
Niles Armstrong, Ivan Blank
Recent work by Serfaty and Serra give a formula for the velocity of the free boundary of the obstacle problem at regular points [Serfaty-Serra 2018], and much older work by King, L…
Perturbed Obstacle Problems in Lipschitz Domains: Linear Stability and Non-degeneracy in Measure
Ivan Blank, Jeremy LeCrone
We consider the classical obstacle problem on bounded, connected Lipschitz domains . We derive quantitative bounds on the changes to contact sets under gene…
Geometry of mean value sets for general divergence form uniformly elliptic operators
Ashok Aryal, Ivan Blank
In the Fermi Lectures on the obstacle problem in 1998, Caffarelli gave a proof of the mean value theorem which extends to general divergence form uniformly elliptic operators. In t…
Mean Value Theorems for Riemannian Manifolds via the Obstacle Problem
Brian Benson, Ivan Blank, Jeremy LeCrone
We develop some of the basic theory for the obstacle problem on Riemannian Manifolds, and we use it to establish a mean value theorem. Our mean value theorem works for a very wide…
The geometry of the triple junction between three fluids in equilibrium
Ivan Blank, Alan Elcrat, Ray Treinen
We conduct an analysis of the blow up at the triple junction of three fluids in equilibrium. Energy minimizers have been shown to exist in the class of functions of bounded variati…