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 Eurasian Math. J., 2012, Volume 3, Number 3, Pages 94–109 (Mi emj97)

This article is cited in 9 scientific papers (total in 9 papers)

Operators in Morrey type spaces and applications

M. A. Ragusa

Dipartimento di Matematica e Informatica, Università di Catania, Catania, Italy

Abstract: We consider partial differential equations with discontinuous coefficients and prove that, if the known term belongs to the Morrey space $L^{p,\lambda}$, the highest order derivatives of the solutions of the equations belong to the same space. As a consequence it is possible to obtain local Hölder continuity for the solutions. Moreover, are discussed some estimates for the derivatives of local minimizers of variational integrals.

Keywords and phrases: parabolic equation, Morrey spaces, well-posedness, discontinuous coefficients.

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Document Type: Article
MSC: Primary 33J30, 35J45, 31B10; Secondary 43A15, 34A30
Received: 18.06.2011
Language: English

Citation: M. A. Ragusa, “Operators in Morrey type spaces and applications”, Eurasian Math. J., 3:3 (2012), 94–109

Citation in format AMSBIB
\Bibitem{Rag12}
\by M.~A.~Ragusa
\paper Operators in Morrey type spaces and applications
\jour Eurasian Math. J.
\yr 2012
\vol 3
\issue 3
\pages 94--109
\mathnet{http://mi.mathnet.ru/emj97}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3024131}
\zmath{https://zbmath.org/?q=an:1273.35109}

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. I. Burenkov, “Recent progress in studying the boundedness of classical operators of real analysis in general Morrey-type spaces. I”, Eurasian Math. J., 3:3 (2012), 11–32
2. V. I. Burenkov, “Recent progress in studying the boundedness of classical operators of real analysis in general Morrey-type spaces. II”, Eurasian Math. J., 4:1 (2013), 21–45
3. V. I. Burenkov, D. K. Darbayeva, E. D. Nursultanov, “Description of interpolation spaces for general local Morrey-type spaces”, Eurasian Math. J., 4:1 (2013), 46–53
4. T. V. Tararykova, “Comments on definitions of general local and global Morrey-type spaces”, Eurasian Math. J., 4:1 (2013), 125–134
5. V. I. Burenkov, E. D. Nursultanov, D. K. Chigambayeva, “Description of the interpolation spaces for a pair of local Morrey-type spaces and their generalizations”, Proc. Steklov Inst. Math., 284 (2014), 97–128
6. V. I. Burenkov, T. V. Tararykova, “An analog of Young's inequality for convolutions of functions for general Morrey-type spaces”, Proc. Steklov Inst. Math., 293 (2016), 107–126
7. V. I. Burenkov, T. V. Tararykova, “Young’s inequality for convolutions in Morrey-type spaces”, Eurasian Math. J., 7:2 (2016), 92–99
8. V. I. Burenkov, D. K. Chigambayeva, E. D. Nursultanov, “Marcinkiewicz-type interpolation theorem and estimates for convolutions for Morrey-type spaces”, Eurasian Math. J., 9:2 (2018), 82–88
9. N. R. Ahmedzade, Z. A. Kasumov, “On the Dirichlet problem for the Laplace equation with the boundary value in Morrey space”, Eurasian Math. J., 9:4 (2018), 9–21
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