On variational and quasi-variational inequalities with multivalued lower order terms and convex functionals

2014 ◽  
Vol 94 ◽  
pp. 12-31 ◽  
Author(s):  
Vy Khoi Le
Keyword(s):  
Variational Inequalities ◽  
Lower Order ◽  
Convex Functionals ◽  
Lower Order Terms

Variational Inequalities with General Multivalued Lower Order Terms Given by Integrals

2011 ◽  
Vol 11 (1) ◽  
pp. 1-24 ◽  
Author(s):  
Vy Khoi
Keyword(s):  
Variational Inequalities ◽  
Lower Order ◽  
Order Term ◽  
Multivalued Function ◽  
Solution Set ◽  
Lower Order Term ◽  
Extremal Solutions ◽  
Lower Order Terms

AbstractThis paper is about the existence and some properties of solutions of variational inequalities associated with the 2nd order inclusiondiv[A(x, ∇u)] + L ∈ f (x, u) in Ω,where the lower order term f (x, u) is a general multivalued function. Both coercive and noncoercive cases are considered. In the noncoercive case, we use a sub-supersolution approach to study the existence, comparison, and other properties of the solution set such as its compactness, directedness, and the existence of extremal solutions.

On Parabolic Variational Inequalities with Multivalued Terms and Convex Functionals

2018 ◽  
Vol 18 (2) ◽  
pp. 269-287 ◽  
Author(s):  
Vy Khoi Le ◽  
Klaus Schmitt
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Lower Order ◽  
Order Term ◽  
Growth Conditions ◽  
Principal Term ◽  
Lower Order Term ◽  
Convex Functional ◽  
Parabolic Variational Inequality ◽  
Convex Functionals

Abstract In this paper, we consider the following parabolic variational inequality containing a multivalued term and a convex functional: Find {u\in L^{p}(0,T;W^{1,p}_{0}(\Omega))} and {f\in F(\cdot,\cdot,u)} such that {u(\cdot,0)=u_{0}} and \langle u_{t}+Au,v-u\rangle+\Psi(v)-\Psi(u)\geq\int_{Q}f(v-u)\,dx\,dt\quad% \text{for all }v\in L^{p}(0,T;W^{1,p}_{0}(\Omega)), where A is the principal term; F is a multivalued lower-order term; {\Psi(u)=\int_{0}^{T}\psi(t,u)\,dt} is a convex functional. Moreover, we study the existence and other properties of solutions of this inequality assuming certain growth conditions on the lower-order term F.

scholarly journals Variational Inequalities with Multivalued Lower Order Terms and Convex Functionals in Orlicz-Sobolev Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Ge Dong ◽  
Xiaochun Fang
Keyword(s):  
Sobolev Spaces ◽  
Lower Order ◽  
Principal Part ◽  
Existence Of Solutions ◽  
Order Term ◽  
Convex Functional ◽  
Polynomial Type ◽  
Convex Functionals ◽  
Order Elliptic Operator ◽  
Lower Order Terms

We consider the existence of solutions of variational inequality form. Findu∈D(J):〈A(u),v-u〉+〈F(u),v-u〉+J(v)-J(u)≥0,∀v∈W1LM(Ω),whose principal part is having a growth not necessarily of polynomial type, whereAis a second-order elliptic operator of Leray-Lions type,Fis a multivalued lower order term, andJis a convex functional. We use subsupersolution methods to study the existence and enclosure of solutions in Orlicz-Sobolev spaces.

Elliptic Variational Inequalities with Discontinuous Multi-Valued Lower Order Terms

2013 ◽  
Vol 13 (1) ◽  
Author(s):  
Siegfried Carl
Keyword(s):  
Variational Inequalities ◽  
Elliptic Operator ◽  
Lower Order ◽  
Second Order ◽  
Order Elliptic Operator ◽  
Elliptic Variational Inequalities ◽  
Inequalities For Operators ◽  
Lower Order Terms

AbstractWe consider multi-valued elliptic variational inequalities for operators of the formu ↦ Au + ∂where A is a second order elliptic operator of Leray-Lions type, and u ↦ ∂

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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