Approximation Methods for the Muskhelishvili Equation

Part of the Frontiers in Mathematics book series (FM)


Let D ⊂ ℝ2 denote a domain bounded by a simple closed piecewise smooth contour Γ and let \( {\bar D} \) := D ∪ Γ. It is well known that many problems in plane elasticity, radar imaging, and theory of slow viscous flows can be reduced to the biharmonic problem
$$ \Delta ^2 U(x,y) = 0, (x,y) \in D, $$
where Δ is the Laplace operator (3.48). We assume that the function U is from the space W p 1 (\( {\bar D} \)) ∪ W p 4 (D). The notation W p k (X) is used for the Sobolev space of k-times differentiable functions on X, the derivatives of which belong to the corresponding space L p (X).


Integral Operator Boundary Problem Biharmonic Equation Biharmonic Function Fredholm Property 
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© Birkhäuser Verlag AG 2008

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