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2009 | 7 | 2 | 249-271
Tytuł artykułu

Optimal time and space regularity for solutions of degenerate differential equations

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We derive optimal regularity, in both time and space, for solutions of the Cauchy problem related to a degenerate differential equation in a Banach space X. Our results exhibit a sort of prevalence for space regularity, in the sense that the higher is the order of regularity with respect to space, the lower is the corresponding order of regularity with respect to time.
Wydawca
Czasopismo
Rocznik
Tom
7
Numer
2
Strony
249-271
Opis fizyczny
Daty
wydano
2009-06-01
online
2009-05-24
Twórcy
Bibliografia
  • [1] Cross R., Multivaluedlinearoperators, Marcel Dekker, Inc., New York-Basel-Hong Kong, 1998
  • [2] Favaron A., Lorenzi A., Gradient estimates for solutions of parabolic differential equations degenerating at infinity, Adv. Differential Equations, 2007, 12, 435–460
  • [3] Favini A., Lorenzi A., Tanabe H., Singular integro-differential equations of parabolic type, Adv. Differential Equations, 2002, 7, 769–798
  • [4] Favini A., Lorenzi A., Tanabe H., Yagi A., An L p-approach to singular linear parabolic equations in bounded domains, Osaka J. Math., 2005, 42, 385–406
  • [5] Favini A., Yagi A., Space and time regularity for degenerate evolution equations, J. Math. Soc. Japan, 1992, 44, 331–350 http://dx.doi.org/10.2969/jmsj/04420331[Crossref]
  • [6] Favini A., Yagi A., Mulltivalued linear operators and degenerate evolution equations, Ann. Mat. Pura Appl. (4), 1993, 163, 353–384 http://dx.doi.org/10.1007/BF01759029[Crossref]
  • [7] Favini A., Yagi A., Degenerate differential equations in Banach spaces, Marcel Dekker, Inc., New York-Basel-Hong Kong, 1999
  • [8] Favini A., Yagi A., Quasilinear degenerate evolution equations in Banach spaces, J. Evol. Equ., 2004, 4, 421–449 http://dx.doi.org/10.1007/s00028-004-0169-4[Crossref]
  • [9] Hille E., Phillips R.S., Functional analysis and semi-groups (revised edition), American Mathematical Society, Providence, R.I., 1957
  • [10] Lorenzi A., Tanabe H., Inverse and direct problems for nonautonomous degenerate integrodifferential equations of parabolic type with Dirichlet boundary conditions, Lect. Notes Pure Appl. Math., 2006, 251, 197–243 http://dx.doi.org/10.1201/9781420011135.ch12[Crossref]
  • [11] Lunardi A., Analytic semigroups and optimal regularity in parabolic problems, Birkhäuser Verlag, Basel, 1995
  • [12] Mel’nikova I.V., The Cauchy problem for an inclusion in Banach spaces and distribution spaces, Sib. Math. J., 2001, 42, 751–765 http://dx.doi.org/10.1023/A:1010453716613[Crossref]
  • [13] Periago F., Global existence, uniqueness, and continuous dependence for a semilinear initial value problem, J. Math. Anal. Appl., 2003, 280, 413–423 http://dx.doi.org/10.1016/S0022-247X(03)00126-4[Crossref]
  • [14] Sinestrari E., On the abstract Cauchy problem of parabolic type in spaces of continuous functions, J. Math. Anal. Appl., 1985, 107, 16–66 http://dx.doi.org/10.1016/0022-247X(85)90353-1[Crossref]
  • [15] Taira K., On a degenerate oblique derivative problem with interior boundary conditions, Proc. Japan Acad., 1976, 52, 484–487 http://dx.doi.org/10.3792/pja/1195518211[Crossref]
  • [16] Taira K., The theory of semigroups with weak singularity and its application to partial differential equations, Tsukuba J. Math., 1989, 13, 513–562
  • [17] Triebel H., Interpolation theory, function spaces, differential operators, North-Holland Publishing Co., Amsterdam-New York, 1978
  • [18] von Wahl W., Gebrochene Potenzen eines elliptischen Operators und parabolische Differentialgleichungen in Raümen hölderstetiger Funktionen, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II, 1972, 231–258 (inGerman)
  • [19] von Wahl W., Neue Resolventenabschätzungen für elliptische Differentialoperatoren und semilineare parabolische Gleichungen, Abh. Math. Sem. Univ. Hamburg, 1977, 46, 179–204 (inGerman) http://dx.doi.org/10.1007/BF02993019[Crossref]
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  • [21] Yagi A., Generation theorem of semigroup for multivalued linear operators, Osaka J. Math., 1991, 28, 385–410
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-009-0018-3
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