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Nonlinear Theory and Its Applications, IEICE
Vol. 5 (2014) No. 1 pp. 47-52



Special section on Recent Progress in Verified Numerical Computations

This paper presents a numerical method to verify the invertibility of a linear elliptic operator. The invertibility of a linearized operator is useful information when verifying the existence of a solution for the corresponding nonlinear elliptic partial differential equations (PDEs). The proposed method is proved on the function spaces more suitable than previous methods. The a posteriori estimate, which is expected to converge to the exact operator norm of the inverse elliptic operators, is obtained by less computational cost than existing methods.

Copyright © 2014 The Institute of Electronics, Information and Communication Engineers

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