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December 2001 A Sharp Existence and Uniqueness Theorem for Linear Fuchsian Partial Differential Equations
Jose Ernie C. LOPE
Tokyo J. Math. 24(2): 477-486 (December 2001). DOI: 10.3836/tjm/1255958188

Abstract

In this paper, we will consider the equation $\mathcal{P}u=f$, where $\mathcal{P}$ is the linear Fuchsian partial differential operator \[ \mathcal{P}=(tD_t)^m+\sum_{j=0}^{m-1}\sum_{|\alpha|\leq m-j}a_{j,\alpha}(t, z)(\mu(t)D_z)^\alpha(tD_t)^j . \] We will give a sharp form of unique solvability in the following sense: we can find a domain $\Omega$ such that if $f$ is defined on $\Omega$, then we can find a unique solution $u$ also defined on $\Omega$.

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Jose Ernie C. LOPE. "A Sharp Existence and Uniqueness Theorem for Linear Fuchsian Partial Differential Equations." Tokyo J. Math. 24 (2) 477 - 486, December 2001. https://doi.org/10.3836/tjm/1255958188

Information

Published: December 2001
First available in Project Euclid: 19 October 2009

zbMATH: 0955.05022
MathSciNet: MR1874984
Digital Object Identifier: 10.3836/tjm/1255958188

Rights: Copyright © 2001 Publication Committee for the Tokyo Journal of Mathematics

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Vol.24 • No. 2 • December 2001
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