On the notion of gradient. I. Essentiality of regularity suppositions
Stanisław Gołąb (1960)
Annales Polonici Mathematici
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Stanisław Gołąb (1960)
Annales Polonici Mathematici
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Wojciech M. Zajączkowski (1990)
Banach Center Publications
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Fuyi Xu, Xiaojing Xu, Jia Yuan (2012)
Applicationes Mathematicae
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We discuss the 3D incompressible micropolar fluid equations, and give logarithmically improved regularity criteria in terms of both the velocity field and the pressure in Morrey-Campanato spaces, BMO spaces and Besov spaces.
Marco Cannone, Changxing Miao, Nicolas Prioux, Baoquan Yuan (2006)
Banach Center Publications
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We study the uniqueness and regularity of Leray-Hopf's weak solutions for the MHD equations with dissipation and resistance in different frameworks. Using different kinds of space-time estimates in conjunction with the Littlewood-Paley-Bony decomposition, we present some general criteria of uniqueness and regularity of weak solutions to the MHD system, and prove the uniqueness and regularity criterion in the framework of mixed space-time Besov spaces by applying Tao's trichotomy method. ...
Sagun Chanillo, Carlos E. Kenig (2008)
Journal of the European Mathematical Society
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We study the composite membrane problem in all dimensions. We prove that the minimizing solutions exhibit a weak uniqueness property which under certain conditions can be turned into a full uniqueness result. Next we study the partial regularity of the solutions to the Euler–Lagrange equation associated to the composite problem and also the regularity of the free boundary for solutions to the Euler–Lagrange equations.
Sadek Gala, Maria Alessandra Ragusa (2016)
Annales Polonici Mathematici
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We prove a regularity criterion for micropolar fluid flows in terms of one partial derivative of the velocity in a Morrey-Campanato space.
Nier, F. (2008)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 34L40, 65L10, 65Z05, 81Q20. This article is concerned with the analysis of the WKB expansion in a classically forbidden region for a one dimensional boundary value Schrodinger equation with a non smooth potential. The assumed regularity of the potential is the one coming from a non linear problem and seems to be the critical one for which a good exponential decay estimate can be proved for the first remainder term. The treatment of...
Emilio Acerbi, Giuseppe Mingione (2001)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Irene Fonseca, Nicola Fusco (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Mariano Giaquinta, Giuseppe Modica (1986/87)
Manuscripta mathematica
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Luca Esposito, Giuseppe Mingione (1998)
Revista Matemática Complutense
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Jarosław L. Bojarski (2011)
Applicationes Mathematicae
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The aim of this paper is to study the problem of regularity of displacement solutions in Hencky plasticity. Here, a non-homogeneous material is considered, where the elastic-plastic properties change discontinuously. In the first part, we have found the extremal relation between the displacement formulation defined on the space of bounded deformation and the stress formulation of the variational problem in Hencky plasticity. In the second part, we prove that the displacement...
D. Bayer, M. Stillman (1987)
Inventiones mathematicae
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Zujin Zhang, Xian Yang (2016)
Annales Polonici Mathematici
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We study the Cauchy problem for the MHD system, and provide two regularity conditions involving horizontal components (or their gradients) in Besov spaces. This improves previous results.
K. Höllig, H.-O. Kreiss (1986)
Mathematische Zeitschrift
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Wiesław Grzegorczyk, Beata Medak, Alexey A. Tret’yakov (2012)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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The theory of p-regularity has approximately twenty-five years’ history and many results have been obtained up to now. The main result of this theory is description of tangent cone to zero set in singular case. However there are numerous nonlinear objects for which the p-regularity condition fails, especially for p > 2. In this paper we generalize the p-regularity notion as a starting point for more detailed consideration based on different p-factor operators constructions. ...