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math.AP2026
Divergence-form equations admitting nowhere Lipschitz weak solutions
Menglan Liao, Baisheng Yan
We study a class of partial differential equations in divergence form that admit highly irregular Lipschitz weak solutions. By reformulating these divergence-form equations as a fi…
math.AP2026
Irregular Diffusions and Loss of Regularity in Polyconvex Gradient Flows
Bin Guo, Seonghak Kim, Baisheng Yan
We investigate diffusion-type partial differential equations that are irregular in the sense that they admit weak solutions which are nowhere smooth, even for prescribed smooth dat…
math.AP2023
On integral convexity, variational solutions and nonlinear semigroups
Seonghak Kim, Baisheng Yan
In this paper we provide a different approach for existence of the variational solutions of the gradient flows associated to functionals on Sobolev spaces studied in \cite{BDDMS20}…