Explicit Sobolev estimates for the Cauchy-Riemann equation on parameters
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초록
Let M be a smoothly bounded pseudoconvex complex man-ifold with a family of almost complex structures {Lγ}γ∈I , 0∈I, which extend smoothly up to bM , the boundary of M , and assume that there is λ∈C∞ (bM ) which is strictly subharmonic with respect to the structure L0|bM in any direction where the Levi-form vanishes on bM . We obtainexplicit estimates for the @-Neumann problem in Sobolev spaces both inspace and parameter variables. Also we get a similar result when M isstrongly pseudoconvex.
Abstract
Let M be a smoothly bounded pseudoconvex complex man-ifold with a family of almost complex structures {Lγ}γ∈I , 0∈I, which extend smoothly up to bM , the boundary of M , and assume that there is λ∈C∞ (bM ) which is strictly subharmonic with respect to the structure L0|bM in any direction where the Levi-form vanishes on bM . We obtainexplicit estimates for the @-Neumann problem in Sobolev spaces both inspace and parameter variables. Also we get a similar result when M isstrongly pseudoconvex.
참고문헌 (11)
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