On a semi-variational method for parabolic equations. II
Ivan Hlaváček (1973)
Aplikace matematiky
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Ivan Hlaváček (1973)
Aplikace matematiky
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Jaroslav Haslinger, Ivan Hlaváček (1976)
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R. A. Artino, J. Barros-Neto (1992)
Annales de l'institut Fourier
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Given a hypoelliptic boundary value problem on with an open set in , , we show by matrix triangulation how to reduce it to two uncoupled first order systems, and how to estimate the eigenvalues of the corresponding matrices. Parametrices for the first order systems are constructed. We then characterize hypoellipticity up to the boundary in terms of the Calderon operator corresponding to the boundary value problem.
Ivan Hlaváček, Michal Křížek (1987)
Aplikace matematiky
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Second order elliptic systems with Dirichlet boundary conditions are solved by means of affine finite elements on regular uniform triangulations. A simple averagign scheme is proposed, which implies a superconvergence of the gradient. For domains with enough smooth boundary, a global estimate is proved in the -norm. For a class of polygonal domains the global estimate can be proven.