Global and local estimates for nonlinear noncoercive elliptic equations with measure data

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)

Abstract

We study nonlinear noncoercive elliptic problems with measure data, proving first that the global estimates already known when the problem is coercive are still true for noncoercive problems. We then prove new estimates, on sets far from the support of the singular part of the right-hand side, in the energy space associated to the operator, which entails additional regularity results on the solutions.

Original languageEnglish
Pages (from-to)129-153
Number of pages25
JournalCommunications in Partial Differential Equations
Volume28
Issue number1-2
DOIs
Publication statusPublished - 1 Jan 2003
Externally publishedYes

Keywords

  • Local estimates
  • Measures
  • Non-coercivity
  • Non-linear elliptic equations

Cite this

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abstract = "We study nonlinear noncoercive elliptic problems with measure data, proving first that the global estimates already known when the problem is coercive are still true for noncoercive problems. We then prove new estimates, on sets far from the support of the singular part of the right-hand side, in the energy space associated to the operator, which entails additional regularity results on the solutions.",
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Global and local estimates for nonlinear noncoercive elliptic equations with measure data. / Droniou, Jérôme.

In: Communications in Partial Differential Equations, Vol. 28, No. 1-2, 01.01.2003, p. 129-153.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Droniou, Jérôme

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AB - We study nonlinear noncoercive elliptic problems with measure data, proving first that the global estimates already known when the problem is coercive are still true for noncoercive problems. We then prove new estimates, on sets far from the support of the singular part of the right-hand side, in the energy space associated to the operator, which entails additional regularity results on the solutions.

KW - Local estimates

KW - Measures

KW - Non-coercivity

KW - Non-linear elliptic equations

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