Estimates on solutions to certain quasilinear equations in divergence form

Tsang Hai Kuo*

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

Abstract

The convergence of approximations to solutions of nonlinear elliptic equations is closely related to the structure of the equations. As examples, we examine certain quasilinear elliptic equations with quadratic growth in the gradient defined on bounded domains. L and H1 estimates on approximating solutions are performed to deduce the convergence to a solution in H01 (Ω) ∩ L (Ω). In some cases, H1 a priori bound can be derived without referring to L estimate. Furthermore, a W 2,p(Ω) bound is also established to deduce the existence of strong solutions in W2,p(Ω) ∩ W0 1,p(Ω).

Original languageEnglish
Pages (from-to)237-243
Number of pages7
JournalTaiwanese Journal of Mathematics
Volume9
Issue number2
DOIs
StatePublished - 06 2005

Keywords

  • Quasilinear elliptic problem
  • Strong solution
  • W estimate

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