Nonexistence results for hyperbolic type inequalities involving the Grushin operator in exterior domains
Date
2021-09-14
Authors
Jleli, Mohamed
Samet, Bessem
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We study the hyperbolic type differential inequality
utt(t, x, y) - Lℓu(t, x, y) ≥ |u(t, x, y)|p, (t, x, y) ∈ (0, ∞) x D1 x D2
under the boundary conditions
u(t, x, y) ≥ ƒ(x), (t, x, y) ∈ (0, ∞) x ∂D1 x D2
u(t, x, y) ≥ g(y), (t, x, y) ∈ (0, ∞) x D1 x ∂D2
where p > 1, Dk = {z ∈ ℝNk : |z| ≥ 1}, K = 1, 2, Nk ≥ 2, ƒ ∈ L1(∂D1), g ∈ L1 (∂D2), and Lℓ, ℓ ∈ ℝ, is the Grushin operator
Lℓu = ∆xu + |x|2ℓ ∆yu.
We obtain sufficient conditions depending on p, ℓ, N1 = N2 = 2; N1 = 2, N2 ≥ 3; N1 ≥ 3, N2 = 2; N1, N1, N2 ≥ 3.
Description
Keywords
Global weak solutions, Hyperbolic type inequalities, Exterior domain, Grushin operator
Citation
Jleli, M., & Samet, B. (2021). Nonexistence results for hyperbolic type inequalities involving the Grushin operator in exterior domains. <i>Electronic Journal of Differential Equations, 2021</i>(75), pp. 1-26.
Rights
Attribution 4.0 International