## Tokyo Journal of Mathematics

- Tokyo J. Math.
- Volume 24, Number 2 (2001), 477-486.

### A Sharp Existence and Uniqueness Theorem for Linear Fuchsian Partial Differential Equations

#### 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 $\Omega$.

#### Article information

**Source**

Tokyo J. Math., Volume 24, Number 2 (2001), 477-486.

**Dates**

First available in Project Euclid: 19 October 2009

**Permanent link to this document**

https://projecteuclid.org/euclid.tjm/1255958188

**Digital Object Identifier**

doi:10.3836/tjm/1255958188

**Mathematical Reviews number (MathSciNet)**

MR1874984

**Zentralblatt MATH identifier**

0955.05022

#### Citation

LOPE, Jose Ernie C. A Sharp Existence and Uniqueness Theorem for Linear Fuchsian Partial Differential Equations. Tokyo J. Math. 24 (2001), no. 2, 477--486. doi:10.3836/tjm/1255958188. https://projecteuclid.org/euclid.tjm/1255958188