The Poisson problem with mixed boundary conditions in Sobolev and Besov spaces in non-smooth domains
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We introduce certain Sobolev-Besov spaces which are particularly well adapted for measuring the smoothness of data and solutions of mixed boundary value problems in Lipschitz domains. In particular, these are used to obtain sharp well-posedness results for the Poisson problem for the Laplacian with mixed boundary conditions on bounded Lipschitz domains which satisfy a suitable geometric condition introduced by R.Brown in (1994). In this context, we obtain results which generalize those by D.Jerison and C.Kenig (1995) as well as E.Fabes, O.Mendez and M.Mitrea (1998). Applications to Hodge theory and the regularity of Green operators are also presented.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/9ea147678fe28bda4e5bd91c02340f03c1c3e6f2
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In Applied Mathematics
- Robert Haller-Dintelmann
- Victor Nistor
- Joachim Rehberg
- Alf Jonsson
- Dorothee Knees
- A. Mazzucato
- P. Auscher
- N. Badr
In Mathematical Physics
- Victor Nistor
- Alf Jonsson
- Dorothee Knees
- Robert Haller-Dintelmann
- A. Mazzucato
- Joachim Rehberg
- P. Auscher
- N. Badr
Citations in the corpus
- 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.”
- Hölder Continuity and Optimal Control for Nonsmooth Elliptic Problems (2009, background): “This means that they often live on nonsmooth domains, the coefficients are nonsmooth and, thirdly, they often exhibit mixed boundary conditions, see [3, 43] and the references cited therein, see also [21, 46].”
- Elliptic and parabolic regularity for second‐ order divergence operators with mixed boundary conditions (2013, background): “It is well known that the interval I depends on the domain [17,33] as well as on ([34] or [35]), and on D [36].”
- The square root problem for second-order, divergence form operators with mixed boundary conditions on Lp (2012, methodology): “Compare also [34, Section 5] for a simple characterization of regular sets in case of space-dimensions 2 and 3, and see also [50].”