Results 1 to 10 of about 474,728 (134)
Boundary regularity for strongly degenerate operators of Grushin type
Electronic Journal of Differential Equations, 2022 We prove Harnack inequality and global regularity results for weak solutions of quasilinear degenerate equations driven by operators of Grushin type with natural growth. Degeneracy is a power of a strong A_infinity weight.
Giuseppe Di Fazio +2 more
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Weighted Caffarelli–Kohn–Nirenberg type inequalities related to Grushin type operators
Advances in Nonlinear Analysis, 2016 We consider the Grushin type operator on ℝxd×ℝyk{\mathbb{R}^{d}_{x}\times\mathbb{R}^{k}_{y}} of the ...
Song Manli, Li Wenjuan
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Regularity and Exponential Growth of Pullback Attractors for Semilinear Parabolic Equations Involving the Grushin Operator [PDF]
Abstract and Applied Analysis, 2012 Considered here is the first initial boundary value problem for a semilinear degenerate parabolic equation involving the Grushin operator in a bounded domain Ω.
Nguyen Dinh Binh
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Electronic Journal of Differential Equations, 2021 We study the hyperbolic type differential inequality $$ u_{tt}(t,x,y)-\mathcal{L}_\ell u(t,x,y)\geq |u(t,x,y)|^p,\quad (t,x,y)\in (0,\infty)\times D_1\times D_2 $$ under the boundary conditions $$\displaylines{ u(t,x,y) \geq f(x),\quad (t,x,y)\in (0 ...
Mohamed Jleli, Bessem Samet
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Bifurcation analysis for degenerate problems with mixed regime and absorption
Bulletin of Mathematical Sciences, 2021 We are concerned with the study of a bifurcation problem driven by a degenerate operator of Baouendi–Grushin type. Due to its degenerate structure, this differential operator has a mixed regime.
Ahmed Alsaedi +2 more
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Journal of Inequalities and Applications, 2020 We examine the weighted Grushin system involving advection terms given by { Δ G u − a ⋅ ∇ G u = ( 1 + ∥ z ∥ 2 ( α + 1 ) ) γ 2 ( α + 1 ) v − p in R n , Δ G v − a ⋅ ∇ G v = ( 1 + ∥ z ∥ 2 ( α + 1 ) ) γ 2 ( α + 1 ) u − q in R n , $$ \textstyle\begin{cases}
Belgacem Rahal
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Infinitely many solutions to critical problems involving the p-Grushin operator
Electronic Journal of Differential EquationsWe consider a critical problem in a bounded domain involving the p-Grushin operator. After a truncation argument, we obtain infinitely many solutions to our problem via Krasnoselskii's genus, extending a previous result of Garcia Azorero and Peral Alonso
Paolo Malanchini +2 more
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Stable weak solutions to weighted Kirchhoff equations of Lane–Emden type
Advances in Difference Equations, 2021 This paper is concerned with the Liouville type theorem for stable weak solutions to the following weighted Kirchhoff equations: − M ( ∫ R N ξ ( z ) | ∇ G u | 2 d z ) div G ( ξ ( z ) ∇ G u ) = η ( z ) | u | p − 1 u , z = ( x , y ) ∈ R N = R N 1 × R N 2 ,
Yunfeng Wei, Hongwei Yang, Hongwang Yu
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Sobolev spaces and boundary-value problems for the curl and gradient-of-divergence operators
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2020 We study boundary value and spectral problems in a bounded domain $G$ with smooth border for operators $\operatorname{rot} +\lambda I$ and $\nabla \operatorname{div} +\lambda I$ in the Sobolev spaces. For $\lambda\neq 0$ these operators are reducible (by
Romen Semenovich Saks
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Liouville-type theorem for Kirchhoff equations involving Grushin operators
Boundary Value Problems, 2020 The aim of this paper is to prove the Liouville-type theorem of the following weighted Kirchhoff equations: 0.1 − M ( ∫ R N ω ( z ) | ∇ G u | 2 d z ) div G ( ω ( z ) ∇ G u ) = f ( z ) e u , z = ( x , y ) ∈ R N = R N 1 × R N 2 $$\begin{aligned} \begin ...
Yunfeng Wei, Caisheng Chen, Hongwei Yang
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