The dirichlet problem in lipschitz domains for higher order elliptic systems with rough coefficients

By Vladimir G. Maz'ya, M. Mitrea, T. Shaposhnikova. 2007

91 citations recorded by the source corpus.

We study the Dirichlet problem, in Lipschitz domains and with boundary data in Besov spaces, for divergence form strongly elliptic systems of arbitrary order with bounded, complex-valued coefficients. A sharp corollary of our main solvability result is that the operator of this problem performs an isomorphism between weighted Sobolev spaces when its coefficients and the unit normal of the boundary belong to the space VMO.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/4550ba0cc1a171d14c98a7d1a07cf33f4932b4ad

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In Applied Mathematics

1. Lixin Yan
2. Xuan Thinh Duong
3. H. Bui
4. Fritz Gesztesy
5. M. Mitrea
6. Dachun Yang
7. Renjin Jiang
8. S. Hofmann

In Computational Theory and Mathematics

1. M. Mitrea
2. Fritz Gesztesy
3. Lixin Yan
4. Xuan Thinh Duong
5. Olaf Post
6. Jussi Behrndt
7. S. Hassi
8. H. D. de Snoo

Citations in the corpus

• A description of all self-adjoint extensions of the Laplacian and Kreĭn-type resolvent formulas on non-smooth domains (2009, background): “The following result has been proved in [91].”
• Calderón reproducing formulas and new Besov spaces associated with operators (2012, background): “[34,36,38]), it would be of considerable interest to extend the results in Proposition 5.”