- journal article metadata
European Mathematical Society Publishing House
2016-10-17 23:45:01
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
18
2016
3
On Hamilton–Jacobi–Bellman equations with convex gradient constraints
Ryan
Hynd
University of Pennsylvania, PHILADELPHIA, UNITED STATES
Henok
Mawi
Howard University, WASHINGTON, UNITED STATES
Fully nonlinear, free boundary problem, Bernstein’s method
We study PDE of the form $\max\{F(D^2u,x)-f(x), H(Du)\}=0$ where $F$ is uniformly elliptic and convex in its first argument, $H$ is convex, $f$ is a given function and $u$ is the unknown. These equations are derived from dynamic programming in a wide class of stochastic singular control problems. In particular, examples of these equations arise in mathematical finance models involving transaction costs, in queuing theory, and spacecraft control problems. The main aspects of this work are to identify conditions under which solutions are uniquely defined and have Lipschitz continuous gradients.
Partial differential equations
Systems theory; control
291
315
10.4171/IFB/365
http://www.ems-ph.org/doi/10.4171/IFB/365