Estimates for Green function and Poisson kernels of higher-order Dirichlet boundary value problems

By Anna Dall’Acqua, Guido Sweers. 2004

81 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/8551ecfd93162eada0790402928be9ffd34dec3a

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Adams' inequalities for bi-Laplacian and extremal functions in dimension four (2009, unknown): “Several useful estimates of G(x,y) are listed here for future reference, see for example [12], namely there exists C > 0 such that for all x, y ∈ Ω , x = y, we have ∣∣G(x,y)∣∣ C log(2+ 1 |x − y| ) , ∣∣∇ G(x, y)∣∣ C|x − y|−i , i 1.”
Positivity and Almost Positivity of Biharmonic Green’s Functions under Dirichlet Boundary Conditions (2007, background): “If n ≥ 5, this fundamental solution can even be interpreted as a Green’s function in Rn, where the Dirichlet boundary conditions at infinity are understood as a suitable decay.”
Powers of Distances to Lower Dimensional Sets as Muckenhoupt Weights (2013, background): “Under different conditions for a domain Ω, weighted norm estimates for solutions of linear and nonlinear equations have been studied by several authors (see for example [5], [6], [7], [18]), where the weight of interest is a power of the distance to the boundary ∂Ω.”
On Positivity for the Biharmonic Operator under Steklov Boundary Conditions (2008, unknown): “Based on several estimates due to Zhao [31, 32] (see also [28, 8]) one may show:”
A priori bounds for semilinear equations and a new class of critical exponents for Lipschitz domains (2007, methodology): “The proof of Theorem 6 is inspired by the recent work of Quittner, Souplet [16] and Dall’Acqua, Sweers [6], see also Bidaut-Véron, Yarur [2] for related results.”