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Demonstrates well-posedness and regularity in degenerate elliptic equations, indicating effective modeling techniques.
Consider the degenerate elliptic operator L δ := − ∂ x 2 − δ 2 x 2 ∂ y 2 L_δ := -∂ ^2_x-δ ^2/x^2∂ ^2_y on Ω := ( 0 , 1 ) × ( 0 , l ) Ω := (0, 1)× (0, l) , for δ > 0 , l > 0 δ >0, l>0 . We prove well-posedness and regularity results for the degenerate elliptic equation L δ u = f L_δ u=f in Ω Ω , u | ∂ Ω = 0 u|∂ Ω=0 using weighted Sobolev spaces K a m K^m_a . In particular, by a proper choice of the parameters in the weighted Sobolev spaces <mml:
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Hengguang Li (2008) studied this question.
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