L²-data Dirichlet problem for weighted form Laplacians

Wojciech Kozłowski

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Displaying similar documents to “L²-data Dirichlet problem for weighted form Laplacians”

The Dirichlet problem in weighted spaces on a dihedral domain

Adam Kubica (2009)

Banach Center Publications

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We examine the Dirichlet problem for the Poisson equation and the heat equation in weighted spaces of Kondrat'ev's type on a dihedral domain. The weight is a power of the distance from a distinguished axis and it depends on the order of the derivative. We also prove a priori estimates.

On the solvability of Dirichlet problem for the weighted p-Laplacian

Dominik Mielczarek, Jerzy Rydlewski, Ewa Szlachtowska (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper we are concerned with the existence and uniqueness of the weak solution for the weighted p-Laplacian. The purpose of this paper is to discuss in some depth the problem of solvability of Dirichlet problem, therefore all proofs are contained in some detail. The main result of the work is the existence and uniqueness of the weak solution for the Dirichlet problem provided that the weights are bounded. Furthermore, under this assumption the solution belongs to the Sobolev space...

Existence of solutions to the Poisson equation in L₂-weighted spaces

Joanna Rencławowicz, Wojciech M. Zajączkowski (2010)

Applicationes Mathematicae

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We consider the Poisson equation with the Dirichlet and the Neumann boundary conditions in weighted Sobolev spaces. The weight is a positive power of the distance to a distinguished plane. We prove the existence of solutions in a suitably defined weighted space.

The Dirichlet problem and weighted spaces. II.

Alois Kufner, Bohumír Opic (1986)

Časopis pro pěstování matematiky

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Solvability of the heat equation in weighted Sobolev spaces

Wojciech M. Zajączkowski (2011)

Applicationes Mathematicae

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The existence of solutions to an initial-boundary value problem to the heat equation in a bounded domain in ℝ³ is proved. The domain contains an axis and the existence is proved in weighted anisotropic Sobolev spaces with weight equal to a negative power of the distance to the axis. Therefore we prove the existence of solutions which vanish sufficiently fast when approaching the axis. We restrict our considerations to the Dirichlet problem, but the Neumann and the third boundary value...

The product of two Dirichlet series

Frédéric Bayart (2004)

Acta Arithmetica

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A note on the fourth moment of Dirichlet L-functions

H. M. Bui, D. R. Heath-Brown (2010)

Acta Arithmetica

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Generalized multiple Dirichlet series and generalized multiple polylogarithms

Kohji Matsumoto, Hirofumi Tsumura (2006)

Acta Arithmetica

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The successive approximation method for the Dirichlet problem in a planar domain

Dagmar Medková (2008)

Applicationes Mathematicae

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The Dirichlet problem for the Laplace equation for a planar domain with piecewise-smooth boundary is studied using the indirect integral equation method. The domain is bounded or unbounded. It is not supposed that the boundary is connected. The boundary conditions are continuous or p-integrable functions. It is proved that a solution of the corresponding integral equation can be obtained using the successive approximation method.

Growth of coefficients of universal Dirichlet series

A. Mouze (2007)

Annales Polonici Mathematici

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We study universal Dirichlet series with respect to overconvergence, which are absolutely convergent in the right half of the complex plane. In particular we obtain estimates on the growth of their coefficients. We can then compare several classes of universal Dirichlet series.