Symmetry and Monotonicity Property of a Solution of (p,q) Laplace Equation with Singular Term

2023/04/21 by Jana, Ritabrata
#35B06 #35B51 #35J92 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.10861

Abstract

This paper examines the behavior of a positive solution u∈ C^1,α(\BarΩ) of the (p,q) Laplace equation with a singular term and zero Dirichlet boundary condition. Specifically, we consider the equation: -div(|∇ u|^p-2∇ u+ a(x) |∇ u|^q-2∇ u) amp;= (g(x))/(u^δ)+h(x)f(u) amp;in \thinspace B_R(x₀), u amp; =0 amp;on ∂ B_R(x₀). We assume that 0<δ<1, 1

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