Apriori evaluations for the DIRICHLET problem associated with a linear elliptic operator

1974 ◽  
Vol 60 (1-6) ◽  
pp. 131-135 ◽  
Author(s):  
G. Albinus ◽  
N. Boboc ◽  
P. Mustatâ
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Operator ◽  
Linear Elliptic Operator

scholarly journals Weak Uniqueness for Elliptic Operators in ℝ3 with Time-Independent Coefficients

2006 ◽  
Vol 74 (1) ◽  
pp. 91-100
Author(s):  
Cristina Giannotti
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Operator ◽  
Elliptic Operators ◽  
Second Order ◽  
Weak Uniqueness

The author gives a proof with analytic means of weak uniqueness for the Dirichlet problem associated to a second order uniformly elliptic operator in ℝ3 with coefficients independent of the coordinate x3 and continuous in ℝ2 {0}.

scholarly journals Approximation of relaxed Dirichlet problems by boundary value problems in perforated domains

1995 ◽  
Vol 125 (1) ◽  
pp. 99-114 ◽  
Author(s):  
Gianni Dal Maso ◽  
Annalisa Malusa
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problems ◽  
Elliptic Operator ◽  
Bounded Domain ◽  
Radon Measure ◽  
Boundary Value ◽  
Approximation Procedure ◽  
Dirichlet Problems ◽  
Perforated Domains ◽  
Positive Radon Measure

Given an elliptic operator L on a bounded domain Ω ⊆ Rn, and a positive Radon measure μ on Ω, not charging polar sets, we discuss an explicit approximation procedure which leads to a sequence of domains Ωh ⊇ Ω with the following property: for every f ∈ H−1(Ω) the sequence uh of the solutions of the Dirichlet problems Luh = f in Ωh, uh = 0 on ∂Ωh, extended to 0 in Ω\Ωh, converges to the solution of the “relaxed Dirichlet problem” Lu + μu = f in Ω, u = 0 on ∂Ω.

Lower Bounds for Solutions of Parabolic Differential Inequalities

1967 ◽  
Vol 19 ◽  
pp. 667-672 ◽  
Author(s):  
Hajimu Ogawa
Keyword(s):  
Hilbert Space ◽  
Differential Operator ◽  
Asymptotic Behaviour ◽  
Elliptic Operator ◽  
Bounded Domain ◽  
Lower Bounds ◽  
Second Order ◽  
Differential Inequalities ◽  
Linear Elliptic Operator ◽  
Image Position

Let P be the parabolic differential operatorwhere E is a linear elliptic operator of second order on D × [0, ∞), D being a bounded domain in Rn. The asymptotic behaviour of solutions u(x, t) of differential inequalities of the form1has been investigated by Protter (4). He found conditions on the functions ƒ and g under which solutions of (1), vanishing on the boundary of D and tending to zero with sufficient rapidity as t → ∞, vanish identically for all t ⩾ 0. Similar results have been found by Lees (1) for parabolic differential inequalities in Hilbert space.

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