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Remainder terms in a higher order Sobolev inequality
Archiv der Mathematik, 2010A remainder term for a higher-order Sobolev embedding is obtained in this paper. More precisely, if \(\Omega\) is a bounded domain in \(\mathbb{R}^N\) with \(\mathbb{C}^m\) boundary (\(m>1\) is an integer), then there exists a constant \(c(\Omega, m)> 0\) such that \(\| u\|^2- S|u|^2_{2^*}\geq C|u|_w\) for any \(u\) in the space \(\{u\in H^m\Omega\mid ...
GAZZOLA, FILIPPO, T. Weth
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Higher order terms in the saddle point approximation
Proceedings of the IEEE, 1967An integral of the type which commonly occurs in radiation theory is evaluated by the method of steepest descent to optain a well-known asymptotic expansion. The coefficients of the first three terms of this expansion are given in terms of functions and derivatives of functions which appear in the integrand; the coefficient of the third term does not ...
R.H. Schafer, R.G. Kouyoumjian
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Higher Order Terms in the Lamb Shift Calculation
Physical Review Letters, 1960Following previously described techniques, the atomic energy level displacements of order alpha (Z alpha )/sup 6/ ln/sup 2/ (Z alpha )mc/sup 2/ have been calculated and yield a result in agreement with that of Layzer. An addition is introduced which corresponds to a change of gauge of the virtual photon defining one-photon Lamb shift and serves to ...
H. M. Fried, D. R. Yennie
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Higher order Hardy-Rellich inequalities with boundary remainder terms
2009We determine boundary remainder terms for some higher order Hardy–Rellich inequalities involving the polyharmonic operator $(−\Delta)^m$. The results are proved by studying suitable auxiliary boundary eigenvalue problems, the optimal constants found may not be the classical Hardy–Rellich ones.
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Dispersion approximation using higher-order Taylor series terms
Applied Optics, 1987J P, Marfice, O R, Baiocchi
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Reduced order and surrogate models for gravitational waves
Living Reviews in Relativity, 2022Manuel Tiglio, Aaron Villanueva
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Operator expansion error estimation by higher-order terms.
The Journal of the Acoustical Society of America, 1992The operator expansion method for quickly solving the Helmholtz boundary value equation was outlined by Milder [J. Acoust. Soc. Am. 89, 529–541 (1991)]. This method was verified by Kaczkowski and Thorsos for impenetrable surface scattering where Kirchhoff and small perturbation theory hold [J. Acoust. Soc. Am. 90, 2258 (A) (1991)]. In this presentation
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Cancer treatment and survivorship statistics, 2014
Ca-A Cancer Journal for Clinicians, 2014Carol E Desantis +2 more
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