منابع مشابه
On Estimates of Biharmonic Functions on Lipschitz and Convex Domains
Abstract. Using Maz’ya type integral identities with power weights, we obtain new boundary estimates for biharmonic functions on Lipschitz and convex domains in R. For n ≥ 8, combined with a result in [S2], these estimates lead to the solvability of the L Dirichlet problem for the biharmonic equation on Lipschitz domains for a new range of p. In the case of convex domains, the estimates allow u...
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We show that a bilinear estimate for biharmonic functions in a Lipschitz domain Ω is equivalent to the solvability of the Dirichlet problem for the biharmonic equation in Ω. As a result, we prove that for any given bounded Lipschitz domain Ω in Rd and 1 < q < ∞, the solvability of the Lq Dirichlet problem for ∆2u = 0 in Ω with boundary data in WA(∂Ω) is equivalent to that of the Lp regularity p...
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In the field of Geometric Function Theory, one can not deny the importance of analytic and univalent functions. The characteristics of these functions including their taylor series expansion, their coefficients in these representations as well as their associated functional inequalities have always attracted the researchers. In particular, Fekete-Szegö inequality is one of such vastly studied a...
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On a bounded pseudoconvex domain in C with a plurisubharmonic Lipschitz defining function, we prove that the ∂̄-Neumann operator is bounded on Sobolev (1/2)-spaces. 0. Introduction LetD be a bounded pseudoconvex domain in C with the standard Hermitian metric. The ∂̄-Neumann operator N for (p, q)-forms is the inverse of the complex Laplacian = ∂̄ ∂̄∗ + ∂̄∗∂̄ , where ∂̄ is the maximal extension of the C...
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ژورنال
عنوان ژورنال: Annales Academiae Scientiarum Fennicae Series A I Mathematica
سال: 1983
ISSN: 0066-1953
DOI: 10.5186/aasfm.1983.0818