Parabolic mixed problems in spaces of generalized smoothness
DOI:
https://doi.org/10.15407/dopovidi2014.06.023Keywords:
generalized smoothness, parabolic mixed problems, spacesAbstract
We prove theorems on a well-posedness of a general parabolic initial-boundary-value problem in some classes of Hilbert spaces of generalized smoothness. The latter is characterized by number parameters and a supplementary function parameter that varies slowly at infinity in Karamata's sense. As an application, we give new sufficient conditions under which some generalized derivatives of a solution to the problem should be continuous.
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Agranovich M. S., Vishik M. I. Uspekhi mat. nauk, 1964, 19, No. 3: 53–161 (in Russian).
Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva n. N. Linear and quasilinear equations of parabolic type. Moscow: Nauka, 1967. (in Russian).
Lions J.-L., Magenes E. Non-homogeneous boundary-value problems and applications. Vol. 2. Berlin: Springer, 1972.
Zhytarashu N. V., Eidelman S. D. Parabolic boundary value problems. Kishinev: Shtiintsa, 1992 (in Russian).
Eidel’man S. D. Parabolic equations. In: Encycl. Math. Sci. Vol. 63. Partial differential equations, VI. Berlin: Springer, 1994: 205–316.
Ivasishen S. D. The Green matrices of parabolic boundary value problems. Kyiv: Vyshcha shkola, 1990 (in Russian).
Hörmander L. Linear partial differential operators. Berlin: Springer, 1963. https://doi.org/10.1007/978-3-642-46175-0
Volevich L. R., Paneyakh B. P. Uspekhi mat. nauk., 1965, 20, No. 1: 3–74 (in Russian).
Lizorkin P. I. Spaces of generalized smoothness. In: Triebel H. Theory of function spaces. Moscow: Mir, 1986: 381–415 (in Russian).
Farkas W., Leopold H.-G. Ann. Mat. Pura Appl., 2006, 185, No. 1: 1–62. https://doi.org/10.1007/s10231-004-0110-z
Mikhailets V. A., Murach A. A. Hörmander spaces, interpolation and elliptic problems. Kyiv: Institute of Mathematics of NAS of Ukraine, 2010. Available as arXiv: 1106.3214. (in Russian).
Mikhailets V. A., Murach A. A. Banach J. Math. Anal., 2012, 6, No. 2: 211–281. https://doi.org/10.15352/bjma/1342210171
Los V., Murach A. A. Meth. Funct. Anal. Topol., 2013, 19, No. 2: 146–160.
Los V. M., Murach A. A. Zb.prats Inst. of Mathematics of NAS of Ukraine, 2013, 10, No. 2: 219–234 (in Ukrainian).
Seneta E. Correctly changing functions. Moscow: Nauka, 1985 (in Russian).
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