Dirichlet Problem for a Class of Nonlinear Degenerate Elliptic Operators with Critical Growth and Logarithmic Perturbation-Qiuzhen College,Tsinghua University

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Elliptic van Diejen difference operators and elliptic hypergeometric integrals of Selberg type
AbstractIn this talk, I propose a class of eigenfunctions for the elliptic van Diejen operators (Ruijsenaars operators of type BC) which are represented by elliptic hypergeometric integrals of Selberg type. They are constructed from simple seed eigenfunctions by integral transformations, thanks to gauge symmetries and kernel function identities of the van Diejen operators. Based on a collaborat...
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Lamé function and elliptic deformation of KdV vertex operators
AbstractIn this talk, we will show a bilinear framework for elliptic soliton solutions which are composed by the Lamé-type plane wave factors.τfunctions in Hirota’s form are derived and vertex operators that generate suchτfunctions are presented. Bilinear identities are constructed and an algorithm to calculate residues and bilinear equations is formulated. These are investigated in detail f...