Layer potentials, the Hodge Laplacian, and global boundary problems in nonsmooth Riemannian manifolds

By D. Mitrea, M. Mitrea, Michael Taylor. 2001

192 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/fb7d1335380dbed3840a37d65f45d3fe6f7df5e7

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In Applied Mathematics

1. P. Auscher
2. S. Hofmann
3. A. Axelsson
4. M. Mitrea
5. Victor Nistor
6. A. Mazzucato
7. Martin Dindos
8. A. Mcintosh

In Computational Theory and Mathematics

1. Victor Nistor
2. A. Mazzucato
3. P. Auscher
4. M. Mitrea
5. Martin Dindos
6. A. Axelsson
7. S. Hofmann
8. Jürgen Saal

Citations in the corpus

• Friedlander's eigenvalue inequalities and the Dirichlet-to-Neumann semigroup (2012, unknown): “We conclude this discussion by an alternative form definition of Dλ in the case where λ 6∈ σ(∆D).”
• The stokes equation in the Lp-setting: Well-posedness and regularity properties (2018, background): “Combining the off-diagonal estimates from Lemma 4, where t 2 is replaced by 2 † , with a rescaled version of the Sobolev embedding for Hodge spaces (see [153]) sectoriality with spectral angle ps < =2 for ps on L.”
• Analyticity of layer potentials and $L^{2}$ solvability of boundary value problems for divergence form elliptic equations with complex $L^{\infty}$ coefficients (2007, methodology): “tained in [JK1], and that of (N2) and (R2) in [KP], but those authors did not use layer potentials. The case of real symmetric coefficients with some smoothness has been treated via layer potentials in [MMT]. In the “non self-adjoint” setting, previous results had been obtained in three special cases.”
• The Cauchy–Riemann equations on product domains (2009, background): “It is known that on a general Lipschitz domain, the ∂-Neumann operator or even the Green’s operator for the Dirichlet problem (see [3, 28]) is not regular near the singular part of the domain.”
• Well-posedness and Regularity for the Elasticity Equation with Mixed Boundary Conditions on Polyhedral Domains and Domains with Cracks (2010, methodology): “See also [21, 22, 45, 43, 48, 53, 65, 67, 68, 87, 88, 92], and [85] for just a few references to applications of the method of layer potentials to non-smooth domains.”
• The Stationary Navier-Stokes System in Nonsmooth Manifolds: The Poisson Problem in Lipschitz and C1 Domains (2004, methodology): “11) and the general discussion contained in §§1-2 of [40].”