Abstract:
In the present paper, Lp estimates are obtained for the solution of a model problem arising in the linearization of the Verigin problem. The proof is based on the application of theorems on Fourier multipliers. The result obtained may be used for the proof of the solvability of the verigin problem in anisotropic Sobolev spaces.
Citation:
E. V. Frolova, “Solvability of Verigin problem in Sobolev spaces”, Boundary-value problems of mathematical physics and related problems of function theory. Part 33, Zap. Nauchn. Sem. POMI, 295, POMI, St. Petersburg, 2003, 180–203; J. Math. Sci. (N. Y.), 127:2 (2005), 1923–1935
\Bibitem{Fro03}
\by E.~V.~Frolova
\paper Solvability of Verigin problem in Sobolev spaces
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~33
\serial Zap. Nauchn. Sem. POMI
\yr 2003
\vol 295
\pages 180--203
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1261}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1983117}
\zmath{https://zbmath.org/?q=an:1162.35461}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2005
\vol 127
\issue 2
\pages 1923--1935
\crossref{https://doi.org/10.1007/s10958-005-0151-x}
Linking options:
https://www.mathnet.ru/eng/znsl1261
https://www.mathnet.ru/eng/znsl/v295/p180
This publication is cited in the following 3 articles:
Murat Tilepiev, Perizat Beisebay, Aliya Aruova, Erbulat Akzhigitov, “The research of a Stefan problem with unknown pressure in a liquid phase”, Nonlinear Analysis: Real World Applications, 55 (2020), 103124
Pruess J., Simonett G., Wilke M., “The Rayleigh-Taylor Instability For the Verigin Problem With and Without Phase Transition”, NoDea-Nonlinear Differ. Equ. Appl., 26:3 (2019), 18
Pruess J., Simonett G., “The Verigin Problem With and Without Phase Transition”, Interface Free Bound., 20:1 (2018), 107–128
Citation in format AMSBIB
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