A computer-assisted proof method of the invertibility to elliptic operators

Akitoshi Takayasu; Shin'ichi Oishi

Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:D1L-D

Session:

Number:816

A computer-assisted proof method of the invertibility to elliptic operators

Akitoshi Takayasu, Shin'ichi Oishi,

pp.816-819

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.816

PDF download (345.3KB)

Summary:

In this talk, a computer-assisted analysis procedure is proposed with respect to the invertibility of some elliptic operators. Based on a verified eigenvalue evaluation for the Laplace operator, the inverse of an elliptic operator is proved with computer-assistance. Whether the operator has its inverse plays important role in computer-assisted proof methods for nonlinear elliptic problems. The invertibility of considered operator is related to some shifted eigenvalue or weighted eigenvalue problems. A computer-assisted analysis method is proposed in this talk. Furthermore, some applications are presented for semilinear elliptic problems.

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