Sobolev and Hölder estimates for homotopy operators of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mover accent="true"><mml:mrow><mml:mo>∂</mml:mo></mml:mrow><mml:mo>‾</mml:mo></mml:mover></mml:math>-equation on convex domains of finite multitype

Yao, Liding

doi:10.1016/j.jmaa.2024.128238

Journal of Mathematical Analysis and Applications

2024

DOI: 10.1016/j.jmaa.2024.128238

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Sobolev and Hölder estimates for homotopy operators of the ∂‾-equation on convex domains of finite multitype

Liding Yao

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On regularity of \overline∂-solutions on 𝑎_{𝑞} domains with 𝐶² boundary in complex manifolds

Gong

2024

Trans. Amer. Math. Soc.

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We study regularity of solutions u u to ∂ ¯ u = f \overline \partial u=f on a relatively compact C 2 C^2 domain D D in a complex manifold of dimension n n , where f f is a ( 0 , q ) (0,q) form. Assume that there are either ( q + 1 ) (q+1) negative or ( n − q ) (n-q) positive Levi eigenvalues at each point of boundary ∂ D \partial D . Under the necessary condition that a locally L 2 L^2 solution exists on the domain, we show the existence of the solutions on the closure of the domain that gain 1 / 2 1/2 derivative when q = 1 q=1 and f f is in the Hölder–Zygmund space Λ r ( D ) \Lambda ^r( D) with r > 1 r>1 . For q > 1 q>1 , the same regularity for the solutions is achieved when ∂ D \partial D is either sufficiently smooth or of ( n − q ) (n-q) positive Levi eigenvalues everywhere on ∂ D \partial D .

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On regularity of \overline∂-solutions on 𝑎_{𝑞} domains with 𝐶² boundary in complex manifolds

Gong

2024

Trans. Amer. Math. Soc.

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Sobolev and Hölder estimates for homotopy operators of the ∂‾-equation on convex domains of finite multitype

Cited by 1 publication

References 60 publications

On regularity of \overline∂-solutions on 𝑎_{𝑞} domains with 𝐶² boundary in complex manifolds

On regularity of \overline∂-solutions on 𝑎_{𝑞} domains with 𝐶² boundary in complex manifolds

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