Weak Solutions for Singular Quasilinear Elliptic Systems

2016/02/12 by Gurpreet Singh, Singh, Gurpreet
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1602.04071

20 pages, This paper contains in Section 2 the results from my previous paper arXiv:1511.03219

arxiv created 2016/02/12 · arxiv updated 2016/02/15

Abstract

We investigate the quasilinear elliptic system -Δ_m u&=u^-pv^-q, u>0 in Ω, -Δ_m v&=u^rv^-s, v>0 in Ω, u=v=0 on ∂Ω, where Ω⊂\mathbb R^N(N≥ 1) is a bounded and smooth domain, 1<m<∞, p, q, r, s>0. Under certain conditions imposed on the exponents we obtain the existence and uniqueness of a weak solution (u, v) with u, v ∈ W₀^{1, m}(Ω)∩ C(Ω). We also investigate the W₀^{1, τ}(Ω) regularity of solution and determine the optimal range of τ≥ m for such regularity.

Citations

• Regularity of Weak Solutions for Singular Elliptic Problems Driven by m-Laplace Operator

Related

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• On the multiplicity of weak solutions for a class of coupled quasilinear elliptic systems
• Weak solutions for a system of quasilinear elliptic equations
• Regularity of Weak Solutions for Singular Elliptic Problems Driven by m-Laplace Operator
• Existence of weak solutions for nonlinear elliptic systems involving the (p(x), q(x))-Laplacian