3 problems

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The $C^{1,b1}$ -rectifiability conjecture for the singular set
Let $\Sigma$ be the singular set of the anisotropic obstacle problem, and let $A$ be the coefficient matrix with ellipticity constants. $C^{1,\alpha}$ -rectifiability conjecture. Th…
Conjectureopenfree-boundary-regularity minimal-surfaces obstacle-problemsarXiv posted 2 days ago
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The conjecture that the remaining thin-obstacle free-boundary set is empty in low dimensions
Let $u$ be a solution to the thin obstacle problem, let $\Gamma(u)$ be its free boundary, and define … Thus, $\Gamma_*(u)$ consists of free-boundary points whose homogeneity is not…
Conjectureopenfree-boundary-regularity frequency-functions thin-obstacle-problemarXiv posted 2 days ago
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Flatness implies smoothness for solutions of the porous medium equation
Let $\rho$ be a solution to the porous medium equation on $[-1,0] \times B_2(0)$ . Assume that there is a nonempty open cone $C$ such that $\rho(t,x) \leq \rho(t,y)$ whenever…
Conjectureopenfree-boundary-regularity parabolic-pdes porous-medium-equationarXiv posted 2 days ago

The C1,b1C^{1,b1}C1,b1-rectifiability conjecture for the singular set