Research Interests. Main theme of research: nonlinear analysis and geometric function theory. This includes the topics listed below. Linear and Nonlinear Elliptic PDEs: A quasiconvex function is a function which has convex sublevel sets.
This paper studies robustly quasiconvex functions, that is, quasiconvex functions which remain quasiconvex under small linear Viscosity characterizations of quasiconvex functions We state Quasiconvex functions and nonlinear pdes our precise denition of a viscosity solution that we use in this QUASICONVEX FUNCTIONS AND NONLINEAR PDES. (Du, D 2 u)minv D 2 uv T v 1, v Du, which characterizes functions which remain quasiconvex under small linear perturbations.
A comparison principle is proved for L. A representation result using stochastic control is also given, and we consider the obstacle problems for L0 CiteSeerX Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. A second order characterization of functions which have convex level sets Abstract: A second order characterization of functions which have convex level sets (quasiconvex functions) results in the operator In two dimensions this is the mean curvature operator, and in any dimension is the first principal curvature of the surface Our main results include a comparison principle for when and a comparison principle for In mathematics, a quasiconvex function is a realvalued function defined on an interval or on a convex subset of a real vector space such that the inverse image of any set of the form (, ) is a convex set.
For a function of a single variable, along any stretch of the curve the highest point is one of the endpoints. The negative of a quasiconvex function Weak convergence methods for nonlinear partial di erential equations. Spencer Frei Summer 2012 In this report, I have collected the proofs that Professor Gantumur Tsogtgerel, Dr. Sverak example of a rankone but not quasiconvex function. . 22 3 Compactness methods for nonlinear PDEs 26 [59 The quasiconvex envelope through 1rstorder partial differential equations which characterize quasiconvexity of nonsmooth functions, (with E.
Barron and R. Goebel) Dynamical Control Systems, Volume 17, Issue 6, 2012, 1693 1706. A uniqueness result for the quasiconvex operator and first order PDEs for convex envelopes Chapter 22 Nonlinear Partial DierentialEquations The ultimatetopic to be touched on in this book is the vastand active eld of nonlinear partial dierential equations.
The quasiconvex envelope through firstorder partial differential equations which characterize quasiconvexity of nonsmooth functions E. N. Barron, R. Goebel, and R. R. Jensen, Discrete and Continuous Dynamical Systems Series B, Volume 17, Issue 6,2012.