3 papers
math.AP2022
The average distance problem with perimeter-to-area ratio penalization
Qiang Du, Xin Yang Lu, Chong Wang
In this paper we consider the functional \begin{equation*} E_{p,\la}(Ω):=\int_Ω\dist^p(x,\pd Ω)\d x+\la \frac{\H^1(\pd Ω)}{\H^2(Ω)}. \end{equation*} Here , $\la>0$ are giv…
math.AP2022
The average distance problem with an Euler elastica penalization
Qiang Du, Xin Yang Lu, Chong Wang
We consider the minimization of an average distance functional defined on a two-dimensional domain with an Euler elastica penalization associated with $\pd Ω$, the boundary of…
math.AP2020
Regularity and monotonicity for solutions to a continuum model of epitaxial growth with nonlocal elastic effects
Yuan Gao, Xin Yang Lu, Chong Wang
We study a nonlocal 4th order degenerate equation deriving from the epitaxial growth on crystalline materials. We first prove the global existence of evolution variational inequali…