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Articles

On non-homogeneous Robin reflection for harmonic functions

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Pages 1699-1714 | Received 26 Jul 2021, Accepted 10 Oct 2021, Published online: 22 Oct 2021

References

  • Cakoni F, Colton D. Qualitative methods in inverse scattering theory. Springer-Verlag Berlin Heidelberg; 2006.
  • Mottin S, Panasenko G, Ganesh SS. Multiscale modeling of light absorption in tissues: limitations of classical homogenization. Approach, Plos One. 2010;5:1–9.
  • Mottin S. An analytical solution of the Laplace equation with Robin conditions by applying Legendre transform. Integral Transform Spec Funct Taylor & Francis. 2016;27(4):289–306. doi:https://doi.org/10.1080/10652469.2015.1121255?.hal-013769999.
  • Alpay D, Behrndt J. Generalized Q-functions and Dirichlet-to-Neumann maps for elliptic differential operators. J Funct Anal. 2009;257:1666–1594.
  • Behrndt J, ter Elst AFM. Dirichlet-to-Neumann maps on bounded Lipschitz domains. J Differ Equ. 2015;259:5903–5926.
  • Beznea L, Pascu MN, Pascu NR. An equivalence between the Dirichlet and the Neumann problem for the Laplace operator. Potential Anal. 2016;44:655–672.
  • Lavrentiev MA, Shabat BV. Methods of the theory of functions of complex variable. Moscow: Nauka; 1973.
  • Sylvester J, Uhlmann G. The Dirichlet to Numann map and applications. In: Colton D, Ewing R, Rundell W, editors. Inverse problems for partial differential equations. Philadelphia; 1990. (Proceedings of SIAM).
  • Aldawsari M, Savina T. On a Dirichlet-to-Neumann and Robin-to-Neumann operators suitable for reflecting harmonic functions subject to a non-homogeneous condition on an arc. J Anal Math Phys. 2019;9:729–745.
  • Davis Ph. The Schwarz function and its applications. MAA; 1979. (Carus Mathematical Monographs).
  • Khavinson D, Lundberg E. Linear holomorphic partial differential equations and classical potential theory. J Amer Math Soc Math Surv Monographs. 2018;214.
  • Savina T. On non-local reflection for elliptic equation of the second order in R2 (the Dirichlet condition). Trans Am Math Soc. 2012;364(5):2443–2460.
  • Belinskiy BP, Savina TV. The Schwarz reflection principle for harmonic functions in R2 subject to the Robin condition. J Math Anal Appl. 2008;348:685–691.
  • Savina TV. A reflection formula for the Helmholtz equation with the Neumann condition. Comput Math Math Phys. 1999;39(4):652–660.
  • Savina T. From reflections to elliptic growth. J Math Anal Appl. 2019;447(2):1419–1433.
  • Diaz JB, Ludford SS. Reflection principles for linear elliptic second order partial differential equations with constant coefficients. Ann Math Pura Appl. 1955;4:87–95.

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