Estimates for fundamental solutions of parabolic equations in non-divergence form
, 2022 Hongjie Dong, Seick Kim, Sungjin Lee
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Lie Group Symmetries as Integral Transforms of Fundamental Solutions [PDF]
We obtain fundamental solutions for PDEs of the form ut = x uxx +f(x)ux ??xru by showing that if the symmetry group of the PDE is nontrivial, it contains a standard integral transform of the fundamental solution. We show that in this case, the problem of
Kelly A Lennox, Mark Craddock
core
Mathematische Zeitschrift, 1988 This is the first part of a series of papers dealing with eigenfunction expansions for the Schrödinger operator \(H=H_ 0+V(x)\), \(H_ 0=- \Delta /2\), where we assume V(x)\(\in {\mathcal B}^{\infty}(R^ n)\) is real-valued, \({\mathcal B}^{\infty}(R^ n)\) denoting the space of smooth functions on \(R^ n\) with bounded derivatives. In this part, we first
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Asymptotic Expansions of Fundamental Solutions in Parabolic Homogenization [PDF]
, 2017 Jun Geng, Zhongwei Shen
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On the Fundamental Solutions to Stokes Equations
Journal of Differential Equations, 1999 The author studies the behaviour of solutions to the stationary Stokes equations which have an isolated singularity. By using the power series expansions of harmonic and biharmonic functions one can describe the precise structure of solutions near singular points.
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The Method of Fundamental Solutions for the 3D Laplace Inverse Geometric Problem on an Annular Domain [PDF]
, 2022 Mojtaba Sajjadmanesh +3 more
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Fundamental solutions of two multidimensional elliptic equations
Electronic Journal of Differential Equations, 2018 We construct fundamental solutions for two-multidimensional elliptic equations. The solutions are written in explicit form via hypergeometric Gauss functions for $\lambda=0$ and via confluent Horn functions for $\lambda\neq 0$. It is proved that the
Ilnur Garipov, Rinat Mavlyaviev
doaj
A simplified calculation for the fundamental solution to the heat equation on the Heisenberg group [PDF]
, 2008 Albert Boggess, Andrew Raich
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Boundedness and continuity of the fundamental solution of the time dependent Schrödinger equation with singular potentials [PDF]
, 1998 Kenji Yajima
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Fundamental solutions and harmonic analysis on nilpotent groups [PDF]
, 1990 Alexander Nagel +2 more
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