On the first stationary boundary-value problem of elasticity in weighted Sobolev spaces in exterior domains of R3

1996 ◽  
Vol 34 (2) ◽  
pp. 183-190 ◽  
Author(s):  
A. Kozhevnikov
Keyword(s):  
Boundary Value Problem ◽  
Sobolev Spaces ◽  
Boundary Value ◽  
Weighted Sobolev Spaces ◽  
Exterior Domains ◽  
Stationary Boundary

scholarly journals Rapidly decreasing behaviour of solutions in nonlinear 3-D-thermoelasticity

1991 ◽  
Vol 43 (1) ◽  
pp. 89-99 ◽  
Author(s):  
Song Jiang
Keyword(s):  
Boundary Value Problem ◽  
Sobolev Spaces ◽  
Initial Value Problem ◽  
Weighted Sobolev Spaces ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Exterior Domains ◽  
Initial Value ◽  
Initial Boundary Value

In this paper we study the asymptotic behaviour, as |x| → ∞, of solutions to the initial value problem in nonlinear three-dimensional thermoelasticity in some weighted Sobolev spaces. We show that under some conditions, solutions decrease fast for each t as x tends to infinity. We also consider the possible extension of the method presented in this paper to the initial boundary value problem in exterior domains.

scholarly journals Multiple solutions for some strongly degenerate second order elliptic equations

2021 ◽  
pp. 1-12
Author(s):  
João R. Santos ◽  
Gaetano Siciliano
Keyword(s):  
Boundary Value Problem ◽  
Bounded Domain ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Multiple Solutions ◽  
Existence Of Solutions ◽  
Weighted Sobolev Spaces ◽  
Degenerate Operator ◽  
Second Order Elliptic Equations ◽  
Strongly Degenerate

We consider a boundary value problem in a bounded domain involving a degenerate operator of the form L ( u ) = − div ( a ( x ) ∇ u ) and a suitable nonlinearity f. The function a vanishes on smooth 1-codimensional submanifolds of Ω where it is not allowed to be C 2 . By using weighted Sobolev spaces we are still able to find existence of solutions which vanish, in the trace sense, on the set where a vanishes.

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