4 papers
Kinodynamic control systems and discontinuities in clearance
Niles Armstrong, Jory Denny, Jeremy LeCrone
We investigate the structure of discontinuities in clearance (or minimum time) functions for nonlinear control systems with general, closed obstacles (or targets). We establish gen…
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…
Properties of Mean Value Sets: Angle Conditions, Blowup Solutions, and Nonconvexity
Niles Armstrong
We study the mean values sets of the second order divergence form elliptic operator with principal coefficients defined as $$a^{ij}_k(x):= \begin{cases} α_k δ^{ij}(x) &x_n>0 β_k δ^…