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.