On the boundary value problem arising in the radially symmetrical filtration of fluid
J. Goncerzewicz (1983)
Applicationes Mathematicae
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J. Goncerzewicz (1983)
Applicationes Mathematicae
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Wojciech M. Zajączkowski (1990)
Banach Center Publications
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Stefan Ebenfeld (2003)
Banach Center Publications
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Andersson Lars, Chruściel Piotr T.
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Abstract We prove existence of the solutions of the constraint equations satisfying "hyperboloidal boundary conditions" using the Choquet-Bruhat-Lichnerowicz-York conformal method and we analyze in detail their differentiability near the conformal boundary. We show that generic "hyperboloidal initial data" display asymptotic behaviour which is not compatible with Penrose's hypothesis of smoothness of ℐ. We also show that a large class of "non-generic" initial data...
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.
Maurizio Chicco, Marina Venturino (2006)
Bollettino dell'Unione Matematica Italiana
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We prove Holder regularity for solutions of mixed boundary value problems for a class of divergence form elliptic equations with discontinuous and unbounded coefficients, in the presence of boundary integrals.
A. Lasota (1980)
Annales Polonici Mathematici
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Khapov, A.P., Shkhanukov-Lafishev, M.Kh. (2001)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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Frédéric Poupaud (1992)
Forum mathematicum
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Francesca Bucci (2008)
Applicationes Mathematicae
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We consider a structural acoustic problem with the flexible wall modeled by a thermoelastic plate, subject to Dirichlet boundary control in the thermal component. We establish sharp regularity results for the traces of the thermal variable on the boundary in case the system is supplemented with clamped mechanical boundary conditions. These regularity estimates are most crucial for validity of the optimal control theory developed by Acquistapace et al. [Adv. Differential Equations, 2005],...
Annegret Glitzky, Rolf Hünlich (2004)
Banach Center Publications
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We investigate stationary energy models in heterostructures consisting of continuity equations for all involved species, of a Poisson equation for the electrostatic potential and of an energy balance equation. The resulting strongly coupled system of elliptic differential equations has to be supplemented by mixed boundary conditions. If the boundary data are compatible with thermodynamic equilibrium then there exists a unique steady state. We prove that in a suitable neighbourhood of...
Piotr Bogusław Mucha (2005)
Banach Center Publications
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We investigate the inviscid limit for the stationary Navier-Stokes equations in a two dimensional bounded domain with slip boundary conditions admitting nontrivial inflow across the boundary. We analyze admissible regularity of the boundary necessary to obtain convergence to a solution of the Euler system. The main result says that the boundary of the domain must be at least C²-piecewise smooth with possible interior angles between regular components less than π.
Otto Liess (1987)
Banach Center Publications
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O. Gil, F. Quirós (2003)
Annales de l'I.H.P. Analyse non linéaire
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Gianni Gilardi, Stephan Luckhaus (1991)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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One proves, in the case of piecewise smooth coefficients, that the time derivative of the solution of the so called dam problem is a measure, extending the result proved by the same authors in the case of Lipschitz continuous coefficients.
L. H. Erbe, H. W. Knobloch (1990)
Annales Polonici Mathematici
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Antontsev, S.N., Meirmanov, A.M., Yurinsky, V.V. (2001)
Portugaliae Mathematica. Nova Série
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