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

LOPE, Jose Ernie C.

Tokyo J. of Math., Tome 24 (2001) no. 2, p. 477-486 / Harvested from Project Euclid

Résumé

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 $\Omega$.

Publié le : 2001-12-15
Classification:

@article{1255958188,
     author = {LOPE, Jose Ernie C.},
     title = {A Sharp Existence and Uniqueness Theorem for Linear Fuchsian Partial Differential Equations},
     journal = {Tokyo J. of Math.},
     volume = {24},
     number = {2},
     year = {2001},
     pages = { 477-486},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1255958188}
}

LOPE, Jose Ernie C. A Sharp Existence and Uniqueness Theorem for Linear Fuchsian Partial Differential Equations. Tokyo J. of Math., Tome 24 (2001) no. 2, pp.  477-486. http://gdmltest.u-ga.fr/item/1255958188/