On some nonlinear nonhomogeneous elliptic unilateral problems involving noncontrollable lower order terms with measure right hand side

2013 ◽  
Vol 40 (2) ◽  
pp. 197-219
Author(s):  
C. Yazough ◽  
E. Azroul ◽  
H. Redwane
Keyword(s):  
Lower Order ◽  
Right Hand ◽  
Unilateral Problems ◽  
Lower Order Terms

scholarly journals Existence of Solutions for Some Nonlinear Elliptic Anisotropic Unilateral Problems with Lower Order Terms

2018 ◽  
Vol 4 (2) ◽  
pp. 171-188 ◽  
Author(s):  
Youssef Akdim ◽  
Chakir Allalou ◽  
Abdelhafid Salmani
Keyword(s):  
Lower Order ◽  
Existence Of Solutions ◽  
Entropy Solutions ◽  
Unilateral Problem ◽  
Nonlinear Elliptic ◽  
Right Hand ◽  
Unilateral Problems ◽  
The Right ◽  
Lower Order Terms

AbstractIn this paper, we prove the existence of entropy solutions for anisotropic elliptic unilateral problem associated to the equations of the form$$ - \sum\limits_{i = 1}^N {{\partial _i}{a_i}(x,u,\nabla u) - } \sum\limits_{i = 1}^N {{\partial _i}{\phi _i}(u) = f,} $$where the right hand side f belongs to L1(Ω). The operator $- \sum\nolimits_{i = 1}^N {{\partial _i}{a_i}\left( {x,u,\nabla u} \right)} $ is a Leray-Lions anisotropic operator and ϕi ∈ C0(ℝ,ℝ).

On the continuity of solutions of the equations of a porous medium and the fast diffusion with weighted and singular lower-order terms

2021 ◽  
Vol 18 (1) ◽  
pp. 104-139
Author(s):  
Yevhen Zozulia
Keyword(s):  
Porous Medium ◽  
Parabolic Equation ◽  
Harnack Inequality ◽  
Lower Order ◽  
Riesz Potential ◽  
Fast Diffusion ◽  
Right Hand ◽  
Continuity Of Solutions ◽  
The Right ◽  
Lower Order Terms

For the parabolic equation $$ \ v\left(x \right)u_{t} -{div({\omega(x)u^{m-1}}} \nabla u) = f(x,t)\: ,\; u\geq{0}\:,\; m\neq{1} $$ we prove the continuity and the Harnack inequality for generalized k solutions, by using the weighted Riesz potential on the right-hand side of the equation.

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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