Differential and Integral Equations

Brezis-Merle type inequality for a weak solution to the $N$-Laplace equation in Lorentz-Zygmund spaces

Norisuke Ioku

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We consider a regularity estimate for a solution of the homogeneous Dirichlet problem for $N$-Laplace equations in a bounded domain $\Omega\subset{\mathbb R}^N$ with external force $f\in L^1(\Omega)$. 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.

Article information

Differential Integral Equations, Volume 22, Number 5/6 (2009), 495-518.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J92: Quasilinear elliptic equations with p-Laplacian
Secondary: 35B65: Smoothness and regularity of solutions 35D30: Weak solutions 35J25: Boundary value problems for second-order elliptic equations 35J70: Degenerate elliptic equations 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)


Ioku, Norisuke. Brezis-Merle type inequality for a weak solution to the $N$-Laplace equation in Lorentz-Zygmund spaces. Differential Integral Equations 22 (2009), no. 5/6, 495--518. https://projecteuclid.org/euclid.die/1356019603

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