Existence of solution for nonlinear elliptic inclusion problems with degenerate coercivity and $$L^{1}$$-data

2022 ◽  
Author(s):  
Youssef Akdim ◽  
Mohammed Belayachi ◽  
Morad Ouboufettal
Keyword(s):  
Existence Of Solution ◽  
Elliptic Inclusion ◽  
Inclusion Problems ◽  
Nonlinear Elliptic ◽  
Degenerate Coercivity

scholarly journals Existence Theorems on Solvability of Constrained Inclusion Problems and Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Teffera M. Asfaw
Keyword(s):  
Reflexive Banach Space ◽  
Existence Theorems ◽  
Maximal Monotone ◽  
Existence Of Solution ◽  
Existence Results ◽  
Uniformly Convex ◽  
Homotopy Invariance ◽  
Inclusion Problems ◽  
Compact Resolvents ◽  
Nonlinear Variational Inequality

LetXbe a real locally uniformly convex reflexive Banach space with locally uniformly convex dual spaceX⁎. LetT:X⊇D(T)→2X⁎be a maximal monotone operator andC:X⊇D(C)→X⁎be bounded and continuous withD(T)⊆D(C). The paper provides new existence theorems concerning solvability of inclusion problems involving operators of the typeT+Cprovided thatCis compact orTis of compact resolvents under weak boundary condition. The Nagumo degree mapping and homotopy invariance results are employed. The paper presents existence results under the weakest coercivity condition onT+C. The operatorCis neither required to be defined everywhere nor required to be pseudomonotone type. The results are applied to prove existence of solution for nonlinear variational inequality problems.

scholarly journals Existence of Solution for Nonlinear Elliptic Equations with Unbounded Coefficients and Data

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
Hicham Redwane
Keyword(s):  
Elliptic Equations ◽  
Existence Result ◽  
Nonlinear Elliptic Equations ◽  
Existence Of Solution ◽  
Unbounded Coefficients ◽  
Renormalized Solution ◽  
Nonlinear Elliptic

An existence result of a renormalized solution for a class of nonlinear elliptic equations is established. The diffusion functions may not be in for a finite value of the unknown and the data belong to .

scholarly journals Existence of solution and iterative approximation of a system of generalized variational-like inclusion problems in semi-inner product spaces

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6051-6070
Author(s):  
Mohd Bhat ◽  
Bisma Zahoor
Keyword(s):  
Iterative Algorithm ◽  
Monotone Operators ◽  
Existence Of Solution ◽  
Inner Product ◽  
Operator Technique ◽  
Product Spaces ◽  
Iterative Approximation ◽  
Generalized Resolvent ◽  
Inclusion Problems ◽  
Inner Product Spaces

In this paper, we consider the system of generalized variational-like inclusion problems in semi-inner product spaces. We define a class of (H,?)-?-monotone operators and its associated class of generalized resolvent operators. Further, using generalized resolvent operator technique, we give the existence of solution of the generalized variational-like inclusion problems. Furthermore, we suggest an iterative algorithm and give the convergence analysis of the sequences generated by the iterative algorithm. The results presented in this paper extend and unify the related known results in the literature.

Ergodic BSDEs driven by G-Brownian motion and applications

2018 ◽  
Vol 18 (06) ◽  
pp. 1850050 ◽  
Author(s):  
Mingshang Hu ◽  
Falei Wang
Keyword(s):  
Brownian Motion ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Infinite Horizon ◽  
Elliptic Partial Differential Equations ◽  
Stochastic Calculus ◽  
Linearization Method ◽  
Existence Of Solution ◽  
Well Posedness ◽  
Nonlinear Elliptic

This paper considers a new kind of backward stochastic differential equations (BSDEs) driven by [Formula: see text]-Brownian motion, which is called ergodic [Formula: see text]-BSDEs. Firstly, the well-posedness of [Formula: see text]-BSDEs with infinite horizon is given by combining a new linearization method with the argument of Briand and Hu [4]. Then, in view of [Formula: see text]-stochastic calculus approach the Feynman–Kac formula for fully nonlinear elliptic partial differential equations (PDEs) is established. Finally, with the help of the aforementioned results we obtain the existence of solution to [Formula: see text]-EBSDE and some applications are also stated.

Two-dimensional elliptic inclusions

1963 ◽  
Vol 59 (4) ◽  
pp. 811-820 ◽  
Author(s):  
R. D. Bhargava ◽  
H. C. Radhakrishna
Keyword(s):  
Potential Energy ◽  
Elastic Field ◽  
Theory Of Elasticity ◽  
Two Dimensional ◽  
Minimum Potential Energy ◽  
Elliptic Inclusion ◽  
Inclusion Problems ◽  
Equilibrium Size ◽  
The Matrix ◽  
Minimum Potential

AbstractThe simple concept of minimum potential energy of the classical theory of elasticity, first applied to solve inclusion problems (1) by one of the authors (R. D. B.), who considered spherical and circular inclusions, has now been extended to solve elliptic inclusion problems. The complex-variable method of determining the elastic field, first enunciated by A. C. Stevenson in the U.K. and N. I. Muskhelishvili in the U.S.S.R., has been used to determine the elastic field in the infinite material (the matrix) around the inclusion. Strain energies are calculated. The equilibrium size of an elliptic inclusion of elastic (Lamé's) constants λ1 and μ1, differing from those of matrix, for which the constants are λ and μ, has been determined.An independent check on the calculations has been made by testing the continuity of normal and shearing stresses. The results also agree with the known results for the much simpler case when inclusion and matrix are of the same material.

Existence results for nonlinear elliptic equations with degenerate coercivity

2003 ◽  
Vol 182 (1) ◽  
pp. 53-79 ◽  
Author(s):  
Angelo Alvino ◽  
Lucio Boccardo ◽  
Vincenzo Ferone ◽  
Luigi Orsina ◽  
Guido Trombetti
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Existence Results ◽  
Nonlinear Elliptic ◽  
Degenerate Coercivity

Two-dimensional elastic inclusion problems

1961 ◽  
Vol 57 (3) ◽  
pp. 669-680 ◽  
Author(s):  
M. A. Jaswon ◽  
R. D. Bhargava
Keyword(s):  
Complex Variable ◽  
Equilibrium Shape ◽  
Elastic Inclusion ◽  
Explicit Solutions ◽  
Two Dimensional ◽  
Elliptic Inclusion ◽  
Inclusion Problems ◽  
Force Method ◽  
Equivalent Inclusion ◽  
Stress Magnification

ABSTRACTAn account is given of Eshelby's point-force method for solving elastic inclusion problems, and of his equations relating an in homogeneity to its equivalent inclusion. The introduction of complex variable formalism enables explicit solutions to be found in various two-dimensional cases. Strain energies are calculated. The equilibrium shape of an elliptic inclusion exhibits an interesting feature not previously expected. A fresh analysis of stress magnification effects is developed.

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