Mitsuhiro T. Nakao, Kouji Hashimoto and Yoshitaka Watanabe:
A Numerical Method to Verify the Invertibility of Linear Elliptic Operators with Applications to Nonlinear Problems,
Computing, Vol.75, Number 1 (July 2005) pp.1-14.
Special issue: GAMM - Workshop on Guaranteed Error-bounds for the Solution of Nonlinear Problems in Applied Mathematics. Guest Editor: Jurgen Herzberger.

In this paper, we propose a numerical method to verify the invertibility of second-order linear elliptic operators. By using the projection and the constructive a priori error estimates, the invertibility condition is formulated as a numerical inequality based upon the existing verification method originally developed by one of the authors. As a useful application of the result, we present a new verification method of solutions for nonlinear elliptic problems, which enables us to simplify the verification process. Several numerical examples that confirm the actual effectiveness of the method are presented.
July 2005

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