Brezis-merle type inequality for a weak solution to the N-laplace equation in Lorentz-zygmund spaces

Norisuke Ioku

Brezis-merle type inequality for a weak solution to the N-laplace equation in Lorentz-zygmund spaces

Norisuke Ioku

SCI - Mathematics

Research output: Contribution to journal › Review article › peer-review

5 Citations (Scopus)

Abstract

We consider a regularity estimate for a solution of the homogeneous Dirichlet problem for N-Laplace equations in a bounded domain ω ⊆ ℝ^N with external force f ∈ L¹(Ω). Introducing the generalized Lorentz-Zygmund space, we show the multiple exponential integrability of the Brezis-Merle type for an entropy solution of the Dirichlet problem of the N-Laplace equation. We also discuss conditions on f that guarantee the solutions are bounded.

Original language	English
Pages (from-to)	495-518
Number of pages	24
Journal	Differential and Integral Equations
Volume	22
Issue number	5-6
Publication status	Published - 2009 May 1

ASJC Scopus subject areas

Analysis
Applied Mathematics

Cite this

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abstract = "We consider a regularity estimate for a solution of the homogeneous Dirichlet problem for N-Laplace equations in a bounded domain ω ⊆ ℝN with external force f ∈ L1(Ω). Introducing the generalized Lorentz-Zygmund space, we show the multiple exponential integrability of the Brezis-Merle type for an entropy solution of the Dirichlet problem of the N-Laplace equation. We also discuss conditions on f that guarantee the solutions are bounded.",

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T1 - Brezis-merle type inequality for a weak solution to the N-laplace equation in Lorentz-zygmund spaces

AU - Ioku, Norisuke

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N2 - We consider a regularity estimate for a solution of the homogeneous Dirichlet problem for N-Laplace equations in a bounded domain ω ⊆ ℝN with external force f ∈ L1(Ω). Introducing the generalized Lorentz-Zygmund space, we show the multiple exponential integrability of the Brezis-Merle type for an entropy solution of the Dirichlet problem of the N-Laplace equation. We also discuss conditions on f that guarantee the solutions are bounded.

AB - We consider a regularity estimate for a solution of the homogeneous Dirichlet problem for N-Laplace equations in a bounded domain ω ⊆ ℝN with external force f ∈ L1(Ω). Introducing the generalized Lorentz-Zygmund space, we show the multiple exponential integrability of the Brezis-Merle type for an entropy solution of the Dirichlet problem of the N-Laplace equation. We also discuss conditions on f that guarantee the solutions are bounded.

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M3 - Review article

AN - SCOPUS:84878198235

SN - 0893-4983

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SP - 495

EP - 518

JO - Differential and Integral Equations

JF - Differential and Integral Equations

IS - 5-6

ER -

Brezis-merle type inequality for a weak solution to the N-laplace equation in Lorentz-zygmund spaces

Abstract

ASJC Scopus subject areas

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