6 papers · 1 filter
The Critical Semilinear Elliptic Equation with Isolated Boundary Singularities II
Hua-Yang Wang, Jingang Xiong
Continuing the work of the second author (2017), we study the Sobolev critical semilinear elliptic equation in the half-space with an isolated boundary singularity and zero Dirichl…
Optimal Weighted Smoothing and Asymptotics of Ancient Solutions for Fast Diffusion Equations
Beomjun Choi, Xiqin Jiang, Hua-Yang Wang +1
The Cauchy--Dirichlet problem for the fast diffusion equation on a smooth bounded domain admits a natural bound in the weighted space , where is the first Dirichle…
A duality approach to gradient Hölder estimates for linear divergence form elliptic equations
Olli Saari, Yuanlin Sun, Hua-Yang Wang +1
We prove a sparse bound in the context of Schauder theory for divergence form elliptic partial differential equations. In addition, we show how an iteration argument inspired by sp…
Solutions to Sobolev Supercritical Nonlinear Schrodinger Equations on an Annulus via a Hopf Reduction Method
Jian Liang, Hua-Yang Wang
This paper investigates the existence of positive solutions with a prescribed mass for nonlinear Schrodinger equations on an annulus, possibly in the Sobolev supercritical regime.…
Sparse gradient bounds for divergence form elliptic equations
Olli Saari, Hua-Yang Wang, Yuanhong Wei
We provide sparse estimates for gradients of solutions to divergence form elliptic partial differential equations in terms of the source data. We give a general result of Meyers (o…
Nonrelativistic Limit of Normalized Solutions to a class of nonlinear Dirac equations
Pan Chen, Yanheng Ding, Qi Guo +1
In this paper, we investigate the nonrelativistic limit of normalized solutions to a nonlinear Dirac equation as given below: \begin{equation*} \begin{cases} &-i c\sum\limits_{k=1}…