scholarly journals A Note on the Displacement Problem of Elastostatics with Singular Boundary Values

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 46 ◽  
Author(s):  
Alfonsina Tartaglione
Keyword(s):  
Elastic Body ◽  
Function Class ◽  
Singular Boundary ◽  
Regular Boundary ◽  
Boundary Values ◽  
Exterior Domains ◽  
Displacement Problem ◽  
Natural Function ◽  
Linear Elastostatics ◽  
Class C

The displacement problem of linear elastostatics in bounded and exterior domains with a non-regular boundary datum a is considered. Precisely, if the elastic body is represented by a domain of class C k ( k ≥ 2 ) of R 3 and a ∈ W 2 − k − 1 / q , q ( ∂ Ω ) , q ∈ ( 1 , + ∞ ) , then it is proved that there exists a solution which is of class C ∞ in the interior and takes the boundary value in a well-defined sense. Moreover, it is unique in a natural function class.

scholarly journals On the Asymptotic Behavior of D-Solutions to the Displacement Problem of Linear Elastostatics in Exterior Domains

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 77
Author(s):  
Vincenzo Coscia
Keyword(s):  
Asymptotic Behavior ◽  
Lipschitz Domain ◽  
Three Dimensional ◽  
Finite Energy ◽  
Asymptotic Behavior Of Solutions ◽  
Exterior Domains ◽  
Displacement Problem ◽  
Linear Elastostatics

We study the asymptotic behavior of solutions with finite energy to the displacement problem of linear elastostatics in a three-dimensional exterior Lipschitz domain.

scholarly journals On the Fredholm Property of the Trace Operators Associated with the Elastic Layer Potentials

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 134 ◽  
Author(s):  
Giulio Starita ◽  
Alfonsina Tartaglione
Keyword(s):  
Elastic Body ◽  
Elastic Layer ◽  
Fredholm Property ◽  
System Of Equations ◽  
Layer Potentials ◽  
Connected Set ◽  
Equilibrium Configurations ◽  
Linear Elastostatics ◽  
Class C

We deal with the system of equations of linear elastostatics, governing the equilibrium configurations of a linearly elastic body. We recall the basics of the theory of the elastic layer potentials and we extend the trace operators associated with the layer potentials to suitable sets of singular densities. We prove that the trace operators defined, for example, on W 1 − k − 1 / q , q ( ∂ Ω ) (with k ≥ 2 , q ∈ ( 1 , + ∞ ) and Ω an open connected set of R 3 of class C k ), satisfy the Fredholm property.

Smooth Boundary Values Along Totally Real Submanifolds

1984 ◽  
Vol 36 (2) ◽  
pp. 240-248 ◽  
Author(s):  
Edgar Lee Stout
Keyword(s):  
Pseudoconvex Domain ◽  
Smooth Boundary ◽  
Regularity Result ◽  
Boundary Values ◽  
Real Submanifolds ◽  
Strongly Pseudoconvex Domain ◽  
Real Submanifold ◽  
Totally Real Submanifold ◽  
Class C ◽  
Totally Real

The main result of this paper is the following regularity result:THEOREM. Let D ⊂ CNbe a bounded, strongly pseudoconvex domain with bD of class Ck, k ≧ 3. Let Σ ⊂ bD be an N-dimensional totally real submanifold, and let f ∊ A(D) satisfy |f| = 1 on Σ, |f| < 1 on. If Σ is of class Cr, 3 ≦ r < k, then the restriction fΣ = f|Σ of f to Σ is of class Cr − 0, and if Σ is of class Ck, then fΣ is of class Ck − 1.Here, of course, A(D) denotes the usual space of functions continuous on , holomorphic on D, and we shall denote by Ak(D), k = 1, 2, …, the space of functions holomorphic on D whose derivatives or order k lie in A(D).

On the traction problem for linear elastostatics in exterior domains

1984 ◽  
Vol 96 (1-2) ◽  
pp. 55-64 ◽  
Author(s):  
Mariarosaria Padula
Keyword(s):  
Continuous Dependence ◽  
Body Force ◽  
The Body ◽  
Well Posedness ◽  
Exterior Domains ◽  
Homogeneous Case ◽  
Linear Elastostatics

SynopsisIn this note, we study the well-posedness of the exterior traction value problem for linear anisotropic non-homogeneous elastostatics. We prove existence and continuous dependence upon the data. In particular, in the isotropic homogeneous case, provided the body force is “simple”, we show that solutions tend to zero uniformly at large spatial distances.

Theorems in linear elastostatics for exterior domains

1961 ◽  
Vol 8 (1) ◽  
pp. 99-119 ◽  
Author(s):  
M. E. Gurtin ◽  
Eli Sternberg
Keyword(s):  
Exterior Domains ◽  
Linear Elastostatics

scholarly journals The critical Fujita number for a semilinear heat equation in exterior domains with homogeneous Neumann boundary values

2000 ◽  
Vol 130 (3) ◽  
pp. 591-602 ◽  
Author(s):  
H. A. Levine ◽  
Q. S. Zhang
Keyword(s):  
Boundary Value Problem ◽  
Global Solutions ◽  
Neumann Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Boundary Values ◽  
Exterior Domains ◽  
Semilinear Heat Equation ◽  
Image Position ◽  
Initial Boundary Value

Let D be a domain in Rn with bounded complement and let n ≠ 2. For the initial-boundary value problem we prove that there are no non-trivial global (non-negative) solutions if 0 < n (p − 1) ≤ 2 and there exist both global non-trivial and non-global solutions if n (p − 1) > 2.

ON THE MAXIMUM MODULUS THEOREM IN LINEAR ELASTOSTATICS FOR EXTERIOR DOMAINS

1996 ◽  
Vol 06 (06) ◽  
pp. 721-728
Author(s):  
GIULIO STARITA
Keyword(s):  
Positive Constant ◽  
Three Dimensional ◽  
Maximum Modulus ◽  
Finite Energy ◽  
Exterior Domains ◽  
Dirichlet Data ◽  
Maximum Value ◽  
Linear Elastostatics ◽  
Maximum Modulus Theorem

This paper deals with the system of linear elastostatics in exterior three-dimensional domains. We prove that the modulus of every solution with finite energy of such a system may be majorized by a positive constant times the maximum value of the modulus of the Dirichlet data at the boundary (maximum modulus theorem).

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