Regularity Results for Nonlinear Elliptic Systems and Applications

Bensoussan, Alain; Frehse, Jens

doi:10.1007/978-3-662-12905-0

Cited by 139 publications

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“…On one hand, inequality (3.6) is closely related to pointwise estimates on Green functions; see [23,24]. On the other hand, a very important consequence of Theorem 3.1 is the following a priori estimate which is independently established in [19] and implicitely in [25].…”

Section: Weak Harnack Inequality For Any Nonnegative Supersolution Umentioning

confidence: 99%

Harnack Inequalities: An Introduction

Kaßmann

2007

Boundary Value Problems

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The aim of this article is to give an introduction to certain inequalities named after Carl Gustav Axel von Harnack. These inequalities were originally defined for harmonic functions in the plane and much later became an important tool in the general theory of harmonic functions and partial differential equations. We restrict ourselves mainly to the analytic perspective but comment on the geometric and probabilistic significance of Harnack inequalities. Our focus is on classical results rather than latest developments. We give many references to this topic but emphasize that neither the mathematical story of Harnack inequalities nor the list of references given here is complete.

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Section: Weak Harnack Inequality For Any Nonnegative Supersolution Umentioning

confidence: 99%

Harnack Inequalities: An Introduction

Kaßmann

2007

Boundary Value Problems

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“…To prove local Hölder continuity for the displacement vector u we will show the following Morrey's condition (see for instance [6]): in the case of two dimensions it is in the form…”

Section: Theorem 53mentioning

confidence: 99%

A first regularity result for the Armstrong–Frederick cyclic hardening plasticity model with Cosserat effects

Chełmiński

Neff

Owczarek

2015

Journal of Mathematical Analysis and Applications

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The purpose of this article is to prove the Hölder continuity up to the boundary of the displacement vector and the microrotation matrix for the quasistatic, rateindependent Armstrong-Frederick cyclic hardening plasticity model with Cosserat effects. This model is of non-monotone and non-associated type. In the case of two space dimensions we use the hole-filling technique of Widman and the Morrey's Dirichlet growth theorem.

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“…From regularity results for elliptic variational equalities (see [3]) it follows that there exists a constant C > 0 such that…”

Section: Theorem 42 Suppose That There Exists a Constantmentioning

confidence: 99%

Generalized Newton methods for the 2D-Signorini contact problem with friction in function space

Kunisch¹,

Stadler²

2005

ESAIM: M2AN

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Abstract. The 2D-Signorini contact problem with Tresca and Coulomb friction is discussed in infinitedimensional Hilbert spaces. First, the problem with given friction (Tresca friction) is considered. It leads to a constraint non-differentiable minimization problem. By means of the Fenchel duality theorem this problem can be transformed into a constrained minimization involving a smooth functional. A regularization technique for the dual problem motivated by augmented Lagrangians allows to apply an infinite-dimensional semi-smooth Newton method for the solution of the problem with given friction. The resulting algorithm is locally superlinearly convergent and can be interpreted as active set strategy. Combining the method with an augmented Lagrangian method leads to convergence of the iterates to the solution of the original problem. Comprehensive numerical tests discuss, among others, the dependence of the algorithm's performance on material and regularization parameters and on the mesh. The remarkable efficiency of the method carries over to the Signorini problem with Coulomb friction by means of fixed point ideas.Mathematics Subject Classification. 49M05, 49M29, 74M10, 74M15, 74B05.

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Regularity Results for Nonlinear Elliptic Systems and Applications

Abstract: Bensoussan, Alain: Regularity results for non linear elliptic systems and applications / Alain Bensoussan; Jens Frehse.

Cited by 139 publications

References 0 publications

Harnack Inequalities: An Introduction

Harnack Inequalities: An Introduction

A first regularity result for the Armstrong–Frederick cyclic hardening plasticity model with Cosserat effects

Generalized Newton methods for the 2D-Signorini contact problem with friction in function space

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