109 citations · 522 across the 51 of their papers we have counts for
8 papers · 1 filter
A Partial Differential Equation Obstacle Problem for the Level Set Approach to Visibility
Adam Oberman, Tiago Salvador
In this article we consider the problem of finding the visibility set from a given point when the obstacles are represented as the level set of a given function. Although the visib…
Approximate homogenization of convex nonlinear elliptic PDEs
Chris Finlay, Adam M. Oberman
We approximate the homogenization of fully nonlinear, convex, uniformly elliptic Partial Differential Equations in the periodic setting, using a variational formula for the optimal…
Approximate homogenization of fully nonlinear elliptic PDEs: estimates and numerical results for Pucci type equations
Chris Finlay, Adam M. Oberman
We are interested in the shape of the homogenized operator for PDEs which have the structure of a nonlinear Pucci operator. A typical operator is $H^{a_1,a_2}(Q,x)…
A partial differential equation for the strictly quasiconvex envelope
Bilal Abbasi, Adam M. Oberman
In a series of papers Barron, Goebel, and Jensen studied Partial Differential Equations (PDE)s for quasiconvex (QC) functions \cite{barron2012functions, barron2012quasiconvex,barro…
A partial differential equation for the rank one convex envelope
Adam M. Oberman, Yuanlong Ruan
In this article we introduce a Partial Differential Equation (PDE) for the rank one convex envelope. Rank one convex envelopes arise in non-convex vector valued variational problem…
Nonlinear elliptic Partial Differential Equations and p-harmonic functions on graphs
Juan J. Manfredi, Adam M. Oberman, Alex P. Svirodov
In this article we study the well-posedness (uniqueness and existence of solutions) of nonlinear elliptic Partial Differential Equations (PDEs) on a finite graph. These results are…
The Dirichlet problem for the convex envelope
Luis Silvestre, Adam M. Oberman
The Convex Envelope of a given function was recently characterized as the solution of a fully nonlinear Partial Differential Equation (PDE). In this article we study a modified pro…
Bulk Burning Rate in Passive - Reactive Diffusion
Peter Constantin, Alexander Kiselev, Adam Oberman +1
We consider a passive scalar that is advected by a prescribed mean zero divergence-free velocity field, diffuses, and reacts according to a KPP-type nonlinear reaction. We introduc…