Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
ISSN-L : 2185-4106
Special section on Recent Progress in Verified Numerical Computations
An improvement of the theorem of a posteriori estimates for inverse elliptic operators
Takehiko KinoshitaYoshitaka WatanabeMitsuhiro T. Nakao
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2014 Volume 5 Issue 1 Pages 47-52


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.

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© 2014 The Institute of Electronics, Information and Communication Engineers
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