16 citations · 38 across the 16 of their papers we have counts for
14 papers · 1 filter
Discontinuous eikonal equations in metric measure spaces
Qing Liu, Nageswari Shanmugalingam, Xiaodan Zhou
In this paper, we study the eikonal equation in metric measure spaces, where the inhomogeneous term is allowed to be discontinuous, unbounded and merely -integrable in the domai…
Hamilton-Jacobi equations in metric spaces
Qing Liu, Xiaodan Zhou
These are lecture notes for our minicourse at OIST Summer Graduate School "Analysis and Partial Differential Equations" on June 12-17, 2023. We give an overview and collect a few i…
Horizontally quasiconvex envelope in the Heisenberg group
Antoni Kijowski, Qing Liu, Xiaodan Zhou
This paper is concerned with a PDE-based approach to the horizontally quasiconvex (h-quasiconvex for short) envelope of a given continuous function in the Heisenberg group. We prov…
Principal eigenvalue problem for infinity Laplacian in metric spaces
Qing Liu, Ayato Mitsuishi
This paper is concerned with the Dirichlet eigenvalue problem associated to the -Laplacian in metric spaces. We establish a direct PDE approach to find the principal eigenv…
Equivalence of solutions of eikonal equation in metric spaces
Qing Liu, Nageswari Shanmugalingam, Xiaodan Zhou
In this paper we prove the equivalence between some known notions of solutions to the eikonal equation and more general analogs of the Hamilton-Jacobi equations in complete and rec…
Horizontal convex envelope in the Heisenberg group and applications to sub-elliptic equations
Qing Liu, Xiaodan Zhou
This paper introduces in a natural way a notion of horizontal convex envelopes of continuous functions in the Heisenberg group. We provide a convexification process to find the env…