Anisotropic Equations with Variable Growth and Coercivity Conditions

2015 ◽  
pp. 107-184
Author(s):  
Stanislav Antontsev ◽  
Sergey Shmarev
Keyword(s):  
Coercivity Conditions

scholarly journals From nonlinear to linearized elasticity via Γ-convergence: The case of multiwell energies satisfying weak coercivity conditions

2014 ◽  
Vol 25 (01) ◽  
pp. 1-38 ◽  
Author(s):  
V. Agostiniani ◽  
T. Blass ◽  
K. Koumatos
Keyword(s):  
Coercivity Conditions ◽  
Coercivity Condition ◽  
Nematic Elastomers ◽  
Linearized Elasticity ◽  
Γ Convergence

Linearized elasticity models are derived, via Γ-convergence, from suitably rescaled nonlinear energies when the corresponding energy densities have a multiwell structure and satisfy a weak coercivity condition, in the sense that the typical quadratic bound from below is replaced by a weaker p bound, 1 < p < 2, away from the wells. This study is motivated by, and our results are applied to, energies arising in the modeling of nematic elastomers.

scholarly journals On a Class of Variational-Hemivariational Inequalities Involving Upper Semicontinuous Set-Valued Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Guo-ji Tang ◽  
Zhong-bao Wang ◽  
Hong-ling Zhang
Keyword(s):  
Existence Of Solutions ◽  
Solution Set ◽  
Hemivariational Inequalities ◽  
Coercivity Conditions ◽  
Upper Semicontinuous ◽  
Set Valued Mappings

This paper is devoted to the various coercivity conditions in order to guarantee existence of solutions and boundedness of the solution set for the variational-hemivariational inequalities involving upper semicontinuous operators. The results presented in this paper generalize and improve some known results.

scholarly journals Brezis pseudomonotone bifunctions and quasi equilibrium problems via penalization

2021 ◽  
Author(s):  
M. Bianchi ◽  
G. Kassay ◽  
R. Pini
Keyword(s):  
Banach Space ◽  
Variational Inequalities ◽  
Equilibrium Problem ◽  
Penalty Method ◽  
Real Banach Space ◽  
Equilibrium Problems ◽  
Existence Results ◽  
Quasi Equilibrium ◽  
Coercivity Conditions ◽  
Usual Equilibrium

AbstractIn this paper we investigate quasi equilibrium problems in a real Banach space under the assumption of Brezis pseudomonotonicity of the function involved. To establish existence results under weak coercivity conditions we replace the quasi equilibrium problem with a sequence of penalized usual equilibrium problems. To deal with the non compact framework, we apply a regularized version of the penalty method. The particular case of set-valued quasi variational inequalities is also considered.

Ambrosetti–Prodi Periodic Problem Under Local Coercivity Conditions

2018 ◽  
Vol 18 (1) ◽  
pp. 169-182 ◽  
Author(s):  
Elisa Sovrano ◽  
Fabio Zanolin
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Problem ◽  
Neumann Boundary ◽  
Continuous Functions ◽  
Periodic Boundary Value Problem ◽  
Multiplicity Result ◽  
Coercivity Conditions

AbstractIn this paper we focus on the periodic boundary value problem associated with the Liénard differential equation{x^{\prime\prime}+f(x)x^{\prime}+g(t,x)=s}, wheresis a real parameter,fandgare continuous functions andgisT-periodic in the variablet. The classical framework of Fabry, Mawhin and Nkashama, related to the Ambrosetti–Prodi periodic problem, is modified to include conditions without uniformity, in order to achieve the same multiplicity result under local coercivity conditions ong. Analogous results are also obtained for Neumann boundary conditions.

scholarly journals Existence results and two step proximal point algorithm for equilibrium problems on Hadamard manifolds

2021 ◽  
Vol 37 (3) ◽  
pp. 393-406
Author(s):  
SULIMAN AL-HOMIDAN ◽  
◽  
QAMRUL HASAN ANSARI ◽  
MONIRUL ISLAM ◽  
◽  
...  
Keyword(s):  
Proximal Point Algorithm ◽  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Coercivity Conditions ◽  
Hadamard Manifolds ◽  
Type Condition ◽  
Proximal Point ◽  
Strong Pseudomonotonicity

"In this paper, we study the existence of solutions of equilibrium problems in the setting of Hadamard manifolds under the pseudomonotonicity and geodesic upper sign continuity of the equilibrium bifunction and under different kinds of coercivity conditions. We also study the existence of solutions of the equilibrium problems under properly quasimonotonicity of the equilibrium bifunction. We propose a two-step proximal point algorithm for solving equilibrium problems in the setting of Hadamard manifolds. The convergence of the proposed algorithm is studied under the strong pseudomonotonicity and Lipschitz-type condition. The results of this paper either extend or generalize several known results in the literature."

scholarly journals Extrapolation of the functional calculus of generalized Dirac operators and related embedding and Littlewood-Paley-type theorems. I

2007 ◽  
Vol 83 (3) ◽  
pp. 297-326 ◽  
Author(s):  
Sergey S. Ajiev
Keyword(s):  
Sufficient Conditions ◽  
Dirac Operators ◽  
Coercivity Conditions ◽  
Embedding Theorems ◽  
Lebesgue Spaces ◽  
Root Model ◽  
Quadratic Estimates ◽  
Resolvent Approach ◽  
Stability Results ◽  
Square Root Model

AbstractSeveral rather general sufficient conditions for the extrapolation of the calculus of generalized Dirac operators from L2 to Lp are established. As consequences, we obtain some embedding theorems, quadratic estimates and Littlewood–Paley theorems in terms of this calculus in Lebesgue spaces. Some further generalizations, utilised in Part II devoted to applications, which include the Kato square root model, are discussed. We use resolvent approach and show the irrelevance of the semigroup one. Auxiliary results include a high order counterpart of the Hilbert identity, the derivation of new forms of ‘off-diagonal’ estimates, and the study of the structure of the model in Lebesgue spaces and its interpolation properties. In particular, some coercivity conditions for forms in Banach spaces are used as a substitution of the ellipticity ones. Attention is devoted to the relations between the properties of perturbed and unperturbed generalized Dirac operators. We do not use any stability results.

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