Stability estimates in     H    0    1     for solutions of elliptic equations in varying domains | Zendy

Arrieta José M. | Zendy; Barbatis Gerassimos | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

Stability estimates in H 0 1 for solutions of elliptic equations in varying domains

Author(s) -

Arrieta José M.,

Barbatis Gerassimos

Publication year - 2013

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.2948

Subject(s) - mathematics , measure (data warehouse) , bounded function , lipschitz continuity , domain (mathematical analysis) , dirichlet distribution , lebesgue measure , elliptic operator , mathematical analysis , boundary (topology) , elliptic curve , lebesgue integration , pure mathematics , class (philosophy) , order (exchange) , stability (learning theory) , lipschitz domain , boundary value problem , finance , database , artificial intelligence , machine learning , computer science , economics

We consider second‐order uniformly elliptic operators subject to Dirichlet boundary conditions. Such operators are considered on a bounded domain Ω and on the domain ϕ (Ω) resulting from Ω by means of a bi‐Lipschitz map ϕ . We consider the solutions u and ũ of the corresponding elliptic equations with the same right‐hand side f ∈ L 2 (Ω ∪ ϕ (Ω)). Under certain assumptions, we estimate the difference ∥ ∇ ũ − ∇ u ∥L 2( Ω ∪ φ ( Ω ) )in terms of certain measure of vicinity of ϕ to the identity map. For domains within a certain class, this provides estimates in terms of the Lebesgue measure of the symmetric difference of ϕ (Ω) and Ω, that is, | ϕ (Ω) △ Ω | . We provide an example that shows that the estimates obtained are in a certain sense sharp. Copyright © 2013 John Wiley & Sons, Ltd.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research