Polyharmonic Boundary Value Problems

By Filippo Gazzola, Hans-Christoph Grunau, Guido Sweers. 2010

646 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/b76f92cf26f97b1088a5c9d36362b95608c5e506

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Higher-order Sobolev embeddings and isoperimetric inequalities (2013, neutral): “The contributions to this field now constitute the corpus of a vast literature, which includes the papers [1,3,5, 9,10,14,15,19,21,23,26,29,30,32,37,39,44,47,48,51,52,54–56,61–63,71,77,86,88,91] and the monographs [16,18,20,45,49,70,80].”
Determining the first order perturbation of a bi-harmonic operator on bounded and unbounded domains from partial data (2013, background): “ electric potential. This type ofoperatorsarisein physicswhen consideringthe equilibrium conﬁgurationofan elastic plate hinged along the boundary. It is also widely used in other physical models, see [6]. In this paper we study the identiﬁability of the ﬁrst order perturbation of a bi-harmonic opera”
Eigenvalues of poly-harmonic operators on variable domains (2012, background): “However, a renewed general interest in higher order operators has been growing in the last decades as it appears in the extensive monograph by Gazzola, Grunau and Sweers [10] devoted to recent developments in the theory of poly-harmonic operators.”
Scattering problems for perturbations of the multidimensional biharmonic operator (2018, background): “As a concrete example, the (linear) beam equation [9] ∂(2) tU + ∆ (2)U +mU = 0 under time-harmonic assumption U(x, t) = u(x)e−iωt results in the equation ∆(2)u+mu = ω(2)u.”
The First Biharmonic Steklov Eigenvalue: Positivity Preserving and Shape Optimization (2011, neutral): “Let us mention that standard elliptic regularity results are available, see [13].”
A Monotonicity Formula and a Liouville-type Theorem for a Fourth Order Supercritical Problem (2013, neutral): “2 in [18]), we have ‖u1‖L1(Br0 ) ≤ C‖u p‖L1(Br0 ) ≤ C (∫”
Weighted integrability of polyharmonic functions (2012, background): “, the books [4,10,12,14], and the papers [11, 20,21,23,17,1,15,33,34].”
Global existence versus blow-up results for a fourth order parabolic PDE involving the Hessian (2015, methodology): “We refer to [18] for the derivation and the physical meaning of these conditions.”