3 problems

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Ivochkina–Trudinger–Wang conjecture on degenerate k-Hessian equations
Ivochkina–Trudinger–Wang conjecture. The condition $f^{\frac{1}{k-1}} \in C^{1,1}(\overline{\Omega})$ should be sufficient for obtaining an existence theorem for the degenerate $k$ …
Conjectureopenfully-nonlinear-pdes hessian-equations neumann-problemarXiv posted 2 days ago
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The DF-index one conjecture for global regularity of the \overline{\partial}-Neumann problem
Let $\Omega$ be a smooth bounded pseudoconvex domain in $\mathbb{C}^{n}$ . Its Diederich--Fornae ss index (DF-index) is the supremum of the exponents for which a defining function a…
Conjectureopencomplex-analysis diederich-fornaess-index neumann-problemarXiv posted 2 days ago
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Neumann disk eigenfunction growth conjecture for $\gamma\geq1$
Let $F^N_{n,m}$ be the $L^2$ -normalized eigenfunctions of the Neumann Laplace operator on the unit disk, with eigenvalues $\lambda^N_{n,m}$ . For a subsequence with…
Conjectureopenlaplace-eigenfunctions neumann-problem unit-diskarXiv posted 2 days ago

Ivochkina–Trudinger–Wang conjecture on degenerate k-Hessian equations