Fatou-type theorems and boundary value problems for elliptic systems in the upper half-space
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- by J. M. Martell, D. Mitrea, I. Mitrea and M. Mitrea
- St. Petersburg Math. J. 31 (2020), 189-222
- DOI: https://doi.org/10.1090/spmj/1592
- Published electronically: February 4, 2020
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Abstract:
This is a survey of recent progress in a program which to date has produced several publications and is aimed at proving general Fatou-type results and establishing the well-posedness of a variety of boundary value problems in the upper half-space ${\mathbb {R}}^n_+$ for second-order, homogeneous, constant complex coefficient, elliptic systems $L$, formulated in a manner that emphasizes pointwise nontangential boundary traces of the null-solutions of $L$ in ${\mathbb {R}}^n_+$.References
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Bibliographic Information
- J. M. Martell
- Affiliation: Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, Consejo Superior de Investigaciones Científicas, C/ Nicolás Cabrera, 13–15, E-28049 Madrid, Spain
- MR Author ID: 671782
- ORCID: 0000-0001-6788-4769
- Email: chema.martell@icmat.es
- D. Mitrea
- Affiliation: Baylor University, Department of Mathematics, One Bear Place #97328, Waco Texas 76798
- MR Author ID: 344702
- ORCID: 0000-0002-0051-7048
- Email: Dorina_Mitrea@baylor.edu
- I. Mitrea
- Affiliation: Department of Mathematics, Temple University, 1805 North Broad Street, Philadelphia, Pennsylvania 19122
- MR Author ID: 634131
- Email: imitrea@temple.edu
- M. Mitrea
- Affiliation: Baylor University, Department of Mathematics, One Bear Place #97328, Waco Texas 76798
- MR Author ID: 341602
- ORCID: 0000-0002-5195-5953
- Email: Marius_Mitrea@baylor.edu
- Received by editor(s): November 25, 2018
- Published electronically: February 4, 2020
- Additional Notes: The first author acknowledges that the research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC agreement no. 615112 HAPDEGMT. He also acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the “Severo Ochoa Programme for Centres of Excellence in R&D” (SEV-2015-0554).
The second author was partially supported by Simons Foundation grant $\#\,$426669
The third author was partially supported by Simons Foundation grants $\#\,$318658 and #616050 and by the NSF grant #1900938
The fourth author was partially supported by Simons Foundation grant $\#\,$637481 - © Copyright 2020 American Mathematical Society
- Journal: St. Petersburg Math. J. 31 (2020), 189-222
- MSC (2010): Primary 31A20, 35C15, 35J57, 42B37, 46E30; Secondary 35B65, 42B25, 42B30, 42B35
- DOI: https://doi.org/10.1090/spmj/1592
- MathSciNet review: 3937496
Dedicated: Dedicated with great pleasure and respect to Vladimir Maz’ya on the occasion of his $80$th birthday