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作者:Jacques Giacomoni , Sweta Tiwari
来源:[J].Electronic Journal of Differential Equations(IF 0.426), 2018, Vol.2018 (44,), pp.1-20DOAJ
摘要:First, we discuss the existence, the uniqueness and the regularityof the weak solution to the following parabolic equation involvingthe fractional p-Laplacian,$$\displaylines{u_t+(-\Delta)_{p}^su +g(x,u)= f(x,u)\quad \text{in } Q_T:=\Omega\times (0,T), \cru = 0 \quad \text{in } \...
作者:Brahim Bougherara , Jacques Giacomoni , Jesus Hernandez
来源:[J].Electronic Journal of Differential Equations(IF 0.426), 2015, Vol.2015 (22), pp.19-30DOAJ
摘要:In this article we study the semilinear singular elliptic problem$$\displaylines{-\Delta u = \frac{p(x)}{u^{\alpha}}\quad \text{in } \Omega \cru = 0\quad \text{on } \partial\Omega,\quad u>0 \text{ in } \Omega,}$$where $\Omega$ is a regular bounded domain of $\mathbb R^{N}$,$\alph...
作者:Jacques Giacomoni , Jyotshana V. Prajapat , Mythily Ramaswamy
来源:[J].Electronic Journal of Differential Equations(IF 0.426), 2007, Vol.Conference (15), pp.107DOAJ
摘要:In this paper, we study the semilinear elliptic problem with critical nonlinearity and an indefinite weight function, namely $$ - Delta u =lambda u + h (x) u^{(n+2)/(n-2)} $$ in a smooth open bounded domain $Omegasubseteq mathbb{R}^n$, $n > 4 $ with Dirichlet boundary conditions ...
作者:Jacques Giacomoni , Jyotshana V. Prajapat , Mythily Ramaswamy
来源:[J].Electronic Journal of Differential Equations(IF 0.426), 2007, Vol.Conference (15), pp.107-126DOAJ
摘要:In this paper, we study the semilinear elliptic problem with critical nonlinearity and an indefinite weight function, namely $$ - Delta u =lambda u + h (x) u^{(n+2)/(n-2)} $$ in a smooth open bounded domain $Omegasubseteq mathbb{R}^n$, $n > 4 $ with Dirichlet boundary conditions ...
作者:Jacques Giacomoni , Divya Goel , K. Sreenadh
来源:[J].Journal of Differential Equations(IF 1.48), 2019Elsevier
摘要:Abstract(#br)The purpose of this article is twofold. First, an issue of regularity of weak solution to the problem ( P ) (see below) is addressed. Secondly, we investigate the question of H s versus C 0 -weighted minimizers of the functional associated to problem ( P ) and then g...
作者:João Marcos do Ó , Jacques Giacomoni , Pawan Kumar Mishra
来源:[J].Nonlinear Differential Equations and Applications NoDEA(IF 0.671), 2019, Vol.26 (4), pp.1-25Springer
摘要:Abstract(#br)In this paper, we study the following nonlocal nonautonomous Hamiltonian system on whole $${\mathbb {R}}$$ R $$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^\frac{1}{2}~ u +u=Q(x) g(v)&{}\quad \text{ in } {\mathbb {R}},\\ (-\Delta )^\frac{1}{2}~ v+v = P(x...
作者:Jacques Giacomoni , Paul Sauvy , Sergey Shmarev
来源:[J].Journal of Mathematical Analysis and Applications(IF 1.05), 2014, Vol.410 (2), pp.607-624Elsevier
摘要:Abstract(#br)We study the homogeneous Dirichlet problem for the quasilinear parabolic equation with the singular absorption term ∂ t u − Δ p u + 1 { u > 0 } u − β = f ( x , u ) in Q T = ( 0 , T ) × Ω . Here Ω ⊂ R d , d ⩾ 1 , is a boun...
作者:Adimurthi , A. Karthik , Jacques Giacomoni
来源:[J].Journal of Differential Equations(IF 1.48), 2016, Vol.260 (11), pp.7739-7799Elsevier
摘要:Abstract(#br)Let n ≥ 2 and Ω ⊂ R n be a bounded domain. Then by Trudinger–Moser embedding, W 0 1 , n ( Ω ) is embedded in an Orlicz space consisting of exponential functions. Consider the corresponding semilinear n -Laplace equation with critical or sub-critical exponen...
作者:Jacques Giacomoni , Sweta Tiwari , Guillaume Warnault
来源:[J].Nonlinear Differential Equations and Applications NoDEA(IF 0.671), 2016, Vol.23 (3)Springer
摘要:Abstract(#br) We discuss the existence and uniqueness of the weak solution of the following quasilinear parabolic equation $$\left\{\begin{array}{ll}u_t-\Delta _{p(x)}u = f(x,u)&\quad \text{in }\quad Q_T \stackrel{{\rm{def}}}{=} (0,T)\times\Omega,\\u = 0 & \quad\text{on}\quad \Si...
作者:Jacques Giacomoni , Ian Schindler , Peter Takáč
来源:[J].Comptes rendus - Mathématique(IF 0.477), 2012, Vol.350 (7-8), pp.383-388Elsevier
摘要:Abstract(#br)We prove the Hölder regularity (Theorem 2.1) for weak solutions to singular quasilinear elliptic equations whose prototype is (P) { − Δ p u = K ( x ) u δ + g ( x ) in Ω ; u | ∂ Ω = 0 , u > 0 in Ω , where Ω is an open bounde...

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