Results 31 to 40 of about 3,531,269 (377)
, 2004 A new approach to the analytic theory of difference equations with rational and elliptic coefficients is proposed. It is based on the construction of canonical meromorphic solutions which are analytical along "thick paths".
Krichever, I.
core +1 more source
Some remarks on singular solutions of nonlinear elliptic equations. I [PDF]
, 2009 The paper concerns singular solutions of nonlinear elliptic ...
Caffarelli, Luis +2 more
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A primal-dual weak Galerkin finite element method for second order elliptic equations in non-divergence form [PDF]
Mathematics of Computation, 2015 This article proposes a new numerical algorithm for second order elliptic equations in non-divergence form. The new method is based on a discrete weak Hessian operator locally constructed by following the weak Galerkin strategy. The numerical solution is
Chunmei Wang, Junping Wang
semanticscholar +1 more source
Einstein equations under polarized $\mathbb U(1)$ symmetry in an elliptic gauge
, 2017 We prove local existence of solutions to the Einstein--null dust system under polarized $\mathbb U(1)$ symmetry in an elliptic gauge. Using in particular the previous work of the first author on the constraint equations, we show that one can identify ...
Huneau, Cécile, Luk, Jonathan
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Hölder Regularity of Solutions to Second-Order Elliptic Equations in Nonsmooth Domains
Boundary Value Problems, 2006 We establish the global Hölder estimates for solutions to second-order elliptic equations, which vanish on the boundary, while the right-hand side is allowed to be unbounded.
Sungwon Cho, Mikhail Safonov
doaj +1 more source
Elliptic solutions to difference non-linear equations and related many-body problems
, 1997 We study algebro-geometric (finite-gap) and elliptic solutions of fully discretized KP or 2D Toda equations. In bilinear form they are Hirota's difference equation for $\tau$-functions.
Krichever, I. +2 more
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Elliptic Dunkl operators, root systems, and functional equations [PDF]
, 1994 We consider generalizations of Dunkl's differential-difference operators associated with groups generated by reflections. The commutativity condition is equivalent to certain functional equations. These equations are solved in many cases.
Buchstaber, V. M. +2 more
core +4 more sources
New non-linear equations and modular form expansion for double-elliptic Seiberg-Witten prepotential
, 2016 Integrable N-particle systems have an important property that the associated Seiberg-Witten prepotentials satisfy the WDVV equations. However, this does not apply to the most interesting class of elliptic and double-elliptic systems.
Aminov, G., Mironov, A., Morozov, A.
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Non-local Gehring lemmas in spaces of homogeneous type and applications [PDF]
, 2018 We prove a self-improving property for reverse H{\"o}lder inequalities with non-local right hand side. We attempt to cover all the most important situations that one encounters when studying elliptic and parabolic partial differential equations as well ...
Auscher, Pascal +3 more
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Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective Epilepsy is increasingly associated with immune dysregulation and inflammation. The T cell receptor (TCR), a key mediator of adaptive immunity, shows repertoire alterations in various immune‐mediated diseases. The unique TCR sequence serves as a molecular barcode for T cells, and clonal expansion accompanied by reduced overall TCR ...
Yong‐Won Shin +12 more
wiley +1 more source