Stability of the solutions of differential equations

Beauzamy, Bernard

Illinois J. Math., Tome 43 (1999) no. 3, p. 151-158 / Harvested from Project Euclid

Résumé

We introduce a new norm (derived from Bombieri's norm for polynomials) on a class of functions on the complex plane. This norm is hilbertian, and can be viewed as a weighted $L_{2}$ norm (or a weighted $l_{2}$ norm). It allows us to give quantitative results of the following sort: If we solve $P(D)u = f$ (with boundary conditions), and if we modify $f$, how is the solution $u$ modified?

Publié le : 1999-03-15
Classification: 35A25, 30C10, 35C99, 46N20

@article{1255985342,
     author = {Beauzamy, Bernard},
     title = {Stability of the solutions of differential equations},
     journal = {Illinois J. Math.},
     volume = {43},
     number = {3},
     year = {1999},
     pages = { 151-158},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1255985342}
}

Beauzamy, Bernard. Stability of the solutions of differential equations. Illinois J. Math., Tome 43 (1999) no. 3, pp.  151-158. http://gdmltest.u-ga.fr/item/1255985342/