Infinite multiplicity of positive solutions for singular nonlinear elliptic equations with convection term and related supercritical problems.
Aranda, Carlos C. (2009)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Qian, Aixia, Li, Chong (2010)
International Journal of Differential Equations
Zhao, Ji-Hong, Zhao, Pei-Hao (2007)
Electronic Journal of Differential Equations (EJDE) [electronic only]
M. Dambrine, G. Vial (2005)
Control and Cybernetics
Gunar Matthies (2007)
ESAIM: Mathematical Modelling and Numerical Analysis
We present families of scalar nonconforming finite elements of arbitrary order with optimal approximation properties on quadrilaterals and hexahedra. Their vector-valued versions together with a discontinuous pressure approximation of order form inf-sup stable finite element pairs of order r for the Stokes problem. The well-known elements by Rannacher and Turek are recovered in the case r=1. A numerical comparison between conforming and nonconforming discretisations will be given. Since higher order...
Kathryn A. Trapp (2008)
ESAIM: Mathematical Modelling and Numerical Analysis
A class of compatible spatial discretizations for solving partial differential equations is presented. A discrete exact sequence framework is developed to classify these methods which include the mimetic and the covolume methods as well as certain low-order finite element methods. This construction ensures discrete analogs of the differential operators that satisfy the identities and theorems of vector calculus, in particular a Helmholtz decomposition theorem for the discrete function spaces. This...
Hongya Gao, Shuang Liang, Yi Cui (2016)
Czechoslovak Mathematical Journal
The paper deals with very weak solutions , , to boundary value problems of the -harmonic equation We show that, under the assumption , , any very weak solution to the boundary value problem () is integrable with provided that is sufficiently close to .
Hassan, M.I. (1984)
International Journal of Mathematics and Mathematical Sciences
E. Lanckau (1974)
Acta Universitatis Carolinae. Mathematica et Physica
Lucio Boccardo (2000)
Banach Center Publications
The aim of this note is to indicate how inequalities concerning the integral of on the subsets where |u(x)| is greater than k () can be used in order to prove summability properties of u (joint work with Daniela Giachetti). This method was introduced by Ennio De Giorgi and Guido Stampacchia for the study of the regularity of the solutions of Dirichlet problems. In some joint works with Thierry Gallouet, inequalities concerning the integral of on the subsets where |u(x)| is less than k () or...
S. A. Nazarov (1993)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Bacuta, C., Mazzucato, A.L., Nistor, V., Zikatanov, L. (2010)
Documenta Mathematica
Jr. J. Douglas, F. A. Milner (1985)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Pierpaolo Esposito (2007)
Annales de l'I.H.P. Analyse non linéaire
Lazarov, R., Tomov, S., Vassilevski, P. (2001)
Computational Methods in Applied Mathematics
Ivan Hlaváček, Michal Křížek (1984)
Aplikace matematiky
Using the stream function, some finite element subspaces of divergence-free vector functions, the normal components of which vanish on a part of the piecewise smooth boundary, are constructed. Applying these subspaces, an internal approximation of the dual problem for second order elliptic equations is defined. A convergence of this method is proved without any assumption of a regularity of the solution. For sufficiently smooth solutions an optimal rate of convergence is proved. The internal approximation...
Jovanović, Boško S., Popović, Branislav Z. (1998)
Novi Sad Journal of Mathematics
Atar, Rami (2001)
Electronic Journal of Probability [electronic only]
Shibata, Tetsutaro (2009)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Baratchart, L., Leblond, J., Marmorat, J.-P. (2006)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]