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A Quantitative Pólya--Szegő Theorem for Tangential Polygons
Changfeng Gui, Yeyao Hu, Qinfeng Li
For a bounded Lipschitz domain , let denote its torsional rigidity, where in and on . We prove a quantit…
Sharp Logarithmic Ultra-analyticity for Fractional and Nonlocal Elliptic Equations
Hongjie Dong, Yeyao Hu, Ming Wang
It is well known that solutions of elliptic equations inherit analyticity from analytic coefficients, while much less is understood about the inheritance of ultra-analytic regulari…
Mixed Torsion on Right Triangles and the Pólya--Szegő Monotonicity Problem for Regular Polygons
Changfeng Gui, Yeyao Hu, Qinfeng Li +1
Motivated by the polygonal Pólya--Szegő conjecture for torsional rigidity, we study two monotonicity problems for torsional rigidity. The first concerns a mixed torsion problem on…
Monotonicity of the first nonzero Steklov eigenvalue of regular -gon with fixed perimeter
Zhuo Cheng, Changfeng Gui, Yeyao Hu +2
We study the first nontrivial Steklov eigenvalue of perimeter-normalized regular \(N\)-gons and show that it is strictly increasing in \(N\). The proof mainly relies on an analytic…
A Lane-Emden system of free boundary type: existence, uniqueness and monotonicity of solutions
Daniele Bartolucci, Yeyao Hu, Aleks Jevnikar +2
We consider a Hamiltonian system of free boundary type, showing first uniform bounds and existence of solutions and of the free boundary. Then, for any smooth and bounded domain, w…
On smooth interior approximation of Sets of Finite Perimeter
Changfeng Gui, Yeyao Hu, Qinfeng Li
In this paper, we prove that for any bounded set of finite perimeter , we can choose smooth sets such that in and \…