Estimate of the Hausdorff measure of the singular set of a solution for a semi-linear elliptic equation associated with superconductivity

Junichi Aramaki

Displaying similar documents to “Estimate of the Hausdorff measure of the singular set of a solution for a semi-linear elliptic equation associated with superconductivity”

Characterization of the boundedness for a family of commutators on $L^{p}$

Song Li (1996)

Colloquium Mathematicae

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Positive solutions to second-order singular differential equations involving the one-dimensional $M$ -Laplace operator.

Tanigawa, Tomoyuki (1999)

Georgian Mathematical Journal

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Estimations of noncontinuable solutions of second order differential equations with $p$ -Laplacian

Eva Pekárková (2010)

Archivum Mathematicum

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We study asymptotic properties of solutions for a system of second differential equations with $p$ -Laplacian. The main purpose is to investigate lower estimates of singular solutions of second order differential equations with $p$ -Laplacian ${(A (t) Φ_{p} (y^{'}))}^{'} + B (t) g (y^{'}) + R (t) f (y) = e (t)$ . Furthermore, we obtain results for a scalar equation.

On the existence of singular solutions.

Bartušek, M., Osička, J. (2001)

Georgian Mathematical Journal

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$L_{\infty}$ -estimate for solutions of nonlinear parabolic systems

Wojciech Zajączkowski (1996)

Banach Center Publications

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We prove existence of weak solutions to nonlinear parabolic systems with p-Laplacians terms in the principal part. Next, in the case of diagonal systems an $L_{\infty}$ -estimate for weak solutions is shown under additional restrictive growth conditions. Finally, $L_{\infty}$ -estimates for weakly nondiagonal systems (where nondiagonal elements are absorbed by diagonal ones) are proved. The $L_{\infty}$ -estimates are obtained by the Di Benedetto methods.

Mappings of finite distortion: composition operator.

Hencl, Stanislav, Koskela, Pekka (2008)

Annales Academiae Scientiarum Fennicae. Mathematica

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Positive solutions of nonlinear elliptic systems

Robert Dalmasso (1993)

Annales Polonici Mathematici

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We study the existence and nonexistence of positive solutions of nonlinear elliptic systems in an annulus with Dirichlet boundary conditions. In particular, $L^{\infty}$ a priori bounds are obtained. We also study a general multiple linear eigenvalue problem on a bounded domain.

Solvability of some singular and nonsingular nonlinear third order boundary value problems

D. O'Regan (1991)

Annales Polonici Mathematici

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Existence of positive solution to certain classes of singular and nonsingular third order nonlinear two point boundary value problems is examined using the idea of Topological Transversality.

Existence theorems for functional differential equations in Banach spaces.

Sghir, A. (2009)

Acta Mathematica Universitatis Comenianae. New Series

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