The Dirichlet problem for elliptic systems with data in Köthe function spaces
dc.creator | Martell, JM | |
dc.creator | Mitrea, D | |
dc.creator | Mitrea, I | |
dc.creator | Mitrea, M | |
dc.date.accessioned | 2021-02-03T16:34:03Z | |
dc.date.available | 2021-02-03T16:34:03Z | |
dc.date.issued | 2016-01-01 | |
dc.identifier.issn | 0213-2230 | |
dc.identifier.doi | http://dx.doi.org/10.34944/dspace/5728 | |
dc.identifier.other | EA8IS (isidoc) | |
dc.identifier.uri | http://hdl.handle.net/20.500.12613/5746 | |
dc.description.abstract | © 2016 European Mathematical Society. We show that the boundedness of the Hardy-Littlewood maximal operator on a Kothe function space X and on its Kothe dual X is equivalent to the well-posedness of the X-Dirichlet and X-Dirichlet problems in Rn + in the class of all second-order, homogeneous, elliptic systems, with constant complex coefficients. As a consequence, we obtain that the Dirichlet problem for such systems is well-posed for boundary data in Lebesgue spaces, variable exponent Lebesgue spaces, Lorentz spaces, Zygmund spaces, as well as their weighted versions. We also discuss a version of the aforementioned result which contains, as a particular case, the Dirichlet problem for elliptic systems with data in the classical Hardy space H1, and the Beurling-Hardy space HAp for p € (1,∞). Based on the well-posedness of the Lp-Dirichlet problem we then prove the uniqueness of the Poisson kernel associated with such systems, as well as the fact that they generate a strongly continuous semigroup in natural settings. Finally, we establish a general Fatou type theorem guaranteeing the existence of the pointwise nontangential boundary trace for null-solutions of such systems. | |
dc.format.extent | 913-970 | |
dc.language.iso | en | |
dc.relation.haspart | Revista Matematica Iberoamericana | |
dc.relation.isreferencedby | European Mathematical Society Publishing House | |
dc.subject | Dirichlet problem | |
dc.subject | second-order elliptic system | |
dc.subject | nontangential maximal function | |
dc.subject | Hardy-Littlewood maximal operator | |
dc.subject | Poisson kernel | |
dc.subject | Green function | |
dc.subject | Kothe function space | |
dc.subject | Muckenhoupt weight | |
dc.subject | Lebesgue space | |
dc.subject | variable exponent Lebesgue space | |
dc.subject | Lorentz space | |
dc.subject | Zygmund space | |
dc.subject | Orlicz space | |
dc.subject | Hardy space | |
dc.subject | Beurling algebra | |
dc.subject | Hardy-Beurling space | |
dc.subject | semigroup | |
dc.subject | Fatou type theorem | |
dc.title | The Dirichlet problem for elliptic systems with data in Köthe function spaces | |
dc.type | Article | |
dc.type.genre | Journal Article | |
dc.relation.doi | 10.4171/rmi/903 | |
dc.ada.note | For Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu | |
dc.date.updated | 2021-02-03T16:34:00Z | |
refterms.dateFOA | 2021-02-03T16:34:04Z |