scholarly journals Combined effects of the Hardy potential and lower order terms in fractional Laplacian equations

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Yingyuan Mi ◽  
Shuibo Huang ◽  
Canyun Huang
Keyword(s):  
Lower Order ◽  
Fractional Laplacian ◽  
Combined Effects ◽  
Hardy Potential ◽  
Laplacian Equations ◽  
Lower Order Terms

scholarly journals Existence of Solutions to Elliptic Problem with Convection Term and Lower-Order Term

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Xiaohua He ◽  
Shuibo Huang ◽  
Qiaoyu Tian ◽  
Yonglin Xu
Keyword(s):  
Dirichlet Problem ◽  
Lower Order ◽  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Order Term ◽  
Combined Effects ◽  
Convection Term ◽  
Bounded Smooth Domain ◽  
Bounded Smooth ◽  
Lower Order Terms

In this paper, we establish the existence of solutions to the following noncoercivity Dirichlet problem − div M x ∇ u + u p − 1 u = − div u E x + f x , x ∈ Ω , u x = 0 , x ∈ ∂ Ω , where Ω ⊂ ℝ N N > 2 is a bounded smooth domain with 0 ∈ Ω , f belongs to the Lebesgue space L m Ω with m ≥ 1 , p > 0 . The main innovation point of this paper is the combined effects of the convection terms and lower-order terms in elliptic equations.

Existence and Regularizing Effect of Degenerate Lower Order Terms in Elliptic Equations Beyond the Hardy Constant

2018 ◽  
Vol 18 (4) ◽  
pp. 775-783 ◽  
Author(s):  
David Arcoya ◽  
Alexis Molino ◽  
Lourdes Moreno-Mérida
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Lower Order ◽  
Dirichlet Boundary Condition ◽  
Elliptic Equations ◽  
Dirichlet Boundary ◽  
Model Problem ◽  
Elliptic Problems ◽  
Hardy Potential ◽  
Lower Order Terms

AbstractIn this paper, we study the regularizing effect of lower order terms in elliptic problems involving a Hardy potential. Concretely, our model problem is the differential equation-\Delta u+h(x)|u|^{p-1}u=\lambda\frac{u}{|x|^{2}}+f(x)\quad\text{in }\Omega,with Dirichlet boundary condition on {\partial\Omega}, where {p>1} and {f\in L^{m}_{h}(\Omega)} (i.e. {|f|^{m}h\in L^{1}(\Omega)}) with {m\geq\frac{p+1}{p}}. We prove that there is a solution of the above problem even for λ greater than the Hardy constant; i.e., {\lambda\geq\mathcal{H}=\frac{(N-2)^{2}}{4}} and nonnegative functions {h\in L^{1}(\Omega)} which could vanish in a subset of Ω. Moreover, we show that all the solutions are in {L^{pm}_{h}(\Omega)}. These results improve and generalize the case {h(x)\equiv h_{0}} treated in [2, 10].

The Regularizing Effect of Lower Order Terms in Elliptic Problems Involving Hardy Potential

2017 ◽  
Vol 17 (2) ◽  
Author(s):  
A. Adimurthi ◽  
Lucio Boccardo ◽  
G. Rita Cirmi ◽  
Luigi Orsina
Keyword(s):  
Lower Order ◽  
Order Term ◽  
Elliptic Problems ◽  
Lower Order Term ◽  
Hardy Potential ◽  
Lower Order Terms

AbstractWe study existence and summability of solutions for elliptic problems with a power-like lower order term and a Hardy potential. We prove that, due to the presence of the lower order term, solutions exist and are more summable under weaker assumptions than those needed for the existence without it.

scholarly journals Hardy potential versus lower order terms in Dirichlet problems: regularizing effects

2022 ◽  
Vol 5 (1) ◽  
pp. 1-14
Author(s):  
David Arcoya ◽  
◽  
Lucio Boccardo ◽  
Luigi Orsina ◽  
◽  
...  
Keyword(s):  
Lower Order ◽  
Potential Versus ◽  
Dirichlet Problems ◽  
Hardy Potential ◽  
Right Hand ◽  
The Right ◽  
Regularizing Effects ◽  
Lower Order Terms

<abstract><p>In this paper, dedicated to Ireneo Peral, we study the regularizing effect of some lower order terms in Dirichlet problems despite the presence of Hardy potentials in the right hand side.</p></abstract>

scholarly journals Nonlinear evolution problems with singular coefficients in the lower order terms

2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Fernando Farroni ◽  
Luigi Greco ◽  
Gioconda Moscariello ◽  
Gabriella Zecca
Keyword(s):  
Lower Order ◽  
Time Horizon ◽  
Existence Result ◽  
Nonlinear Evolution ◽  
Order Term ◽  
Time Behavior ◽  
Infinite Time ◽  
Singular Coefficient ◽  
Singular Coefficients ◽  
Lower Order Terms

AbstractWe consider a Cauchy–Dirichlet problem for a quasilinear second order parabolic equation with lower order term driven by a singular coefficient. We establish an existence result to such a problem and we describe the time behavior of the solution in the case of the infinite–time horizon.

scholarly journals Existence results for nonlinear degenerate elliptic equations with lower order terms

2020 ◽  
Vol 10 (1) ◽  
pp. 301-310
Author(s):  
Weilin Zou ◽  
Xinxin Li
Keyword(s):  
Lower Order ◽  
Elliptic Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Regularity Of Solutions ◽  
Degenerate Elliptic Equations ◽  
Degenerate Elliptic ◽  
Initial Boundary Value ◽  
Lower Order Terms ◽  
Nonlinear Degenerate

Abstract In this paper, we prove the existence and regularity of solutions of the homogeneous Dirichlet initial-boundary value problem for a class of degenerate elliptic equations with lower order terms. The results we obtained here, extend some existing ones of [2, 9, 11] in some sense.

Zero correlation with lower-order terms for automorphic L-functions

2016 ◽  
Vol 12 (01) ◽  
pp. 27-55
Author(s):  
Timothy L. Gillespie ◽  
Yangbo Ye
Keyword(s):  
Lower Order ◽  
Product Formula ◽  
Cuspidal Representation ◽  
Zero Correlation ◽  
Lower Order Terms ◽  
Refined Version ◽  
Low Order

Let [Formula: see text] be a self-contragredient automorphic cuspidal representation of [Formula: see text] for [Formula: see text]. Using a refined version of the Selberg orthogonality, we recompute the [Formula: see text]-level correlation of high non-trivial zeros of the product [Formula: see text]. In the process, we are able to extract certain low-order terms which suggest the asymptotics of these statistics are not necessarily universal, but depend upon the conductors of the representations and hence the ramification properties of the local components coming from each [Formula: see text]. The computation of these lower-order terms is unconditional as long as all [Formula: see text].

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