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Regularity Theory for Elliptic PDE

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Title: Regularity Theory for Elliptic PDE
Description: One of the most basic mathematical questions in PDE is that of regularity. A classical example is Hilbert's XIXth problem, stated in 1900, which was solved by De Giorgi and Nash in the 1950's. The question of regularity has been a central line of research in elliptic PDE during the second half of the 20th century and has influenced many areas of mathematics linked one way or another with PDE. This text aims to provide a self-contained introduction to the regularity theory for elliptic PDE, focusing on the main ideas rather than proving all results in their greatest generality. It can be seen as a bridge between an elementary PDE course and more advanced books. The book starts with a short review of the Laplace operator and harmonic functions. The theory of Schauder estimates is developed next, but presented with various proofs of the results. Nonlinear elliptic PDE are covered in the following, both in the variational and non-variational setting and, finally, the obstacle problem is studied in detail, establishing the regularity of solutions and free boundaries.
Authors: Xavier Fernández-Real, Xavier Ros-Oton
Resource Type: eBook.
Subjects: Differential equations, Partial
Categories: MATHEMATICS / Differential Equations / Partial, MATHEMATICS / Mathematical Analysis, MATHEMATICS / Functional Analysis
Database: eBook Collection (EBSCOhost)
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  – Type: ebook-pdf
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  Availability: 0
Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 3808249
RelevancyScore: 1110
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1109.74133300781
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  Data: Regularity Theory for Elliptic PDE
– Name: Abstract
  Label: Description
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  Data: One of the most basic mathematical questions in PDE is that of regularity. A classical example is Hilbert's XIXth problem, stated in 1900, which was solved by De Giorgi and Nash in the 1950's. The question of regularity has been a central line of research in elliptic PDE during the second half of the 20th century and has influenced many areas of mathematics linked one way or another with PDE. This text aims to provide a self-contained introduction to the regularity theory for elliptic PDE, focusing on the main ideas rather than proving all results in their greatest generality. It can be seen as a bridge between an elementary PDE course and more advanced books. The book starts with a short review of the Laplace operator and harmonic functions. The theory of Schauder estimates is developed next, but presented with various proofs of the results. Nonlinear elliptic PDE are covered in the following, both in the variational and non-variational setting and, finally, the obstacle problem is studied in detail, establishing the regularity of solutions and free boundaries.
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  Data: <searchLink fieldCode="AR" term="%22Xavier+Fernández-Real%22">Xavier Fernández-Real</searchLink><br /><searchLink fieldCode="AR" term="%22Xavier+Ros-Oton%22">Xavier Ros-Oton</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Differential+equations%2C+Partial%22">Differential equations, Partial</searchLink>
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RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 510
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Differential equations, Partial
        Type: general
    Titles:
      – TitleFull: Regularity Theory for Elliptic PDE
        Type: main
  BibRelationships:
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      – PersonEntity:
          Name:
            NameFull: Xavier Fernández-Real
      – PersonEntity:
          Name:
            NameFull: Xavier Ros-Oton
      – PersonEntity:
          Name:
            NameFull: Xavier Fernández-Real
      – PersonEntity:
          Name:
            NameFull: Xavier Ros-Oton
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2022
            – D: 07
              M: 06
              Type: profile
              Y: 2024
          Identifiers:
            – Type: isbn-print
              Value: 9783985470280
            – Type: isbn-electronic
              Value: 9783985475285
          Titles:
            – TitleFull: Regularity Theory for Elliptic PDE
              Type: main
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