By the aid of Aleksandrov–Pucci maximum principle for linear elliptic operators, we derive L∞-a priori estimate and uniqueness for strong solutions to the Dirichlet problem for quasilinear strictly elliptic equations with Carath´eodory’s coefficients. The results obtained compose a preliminary step towards the study of strong solvability (in Sobolev or Morrey spaces) of boundary value problems for quasilinear elliptic operators with discontinuous coefficients.
L^infty-estimates for strong solutions to quasilinear elliptic equations
SOFTOVA Lyoubomira
1999
Abstract
By the aid of Aleksandrov–Pucci maximum principle for linear elliptic operators, we derive L∞-a priori estimate and uniqueness for strong solutions to the Dirichlet problem for quasilinear strictly elliptic equations with Carath´eodory’s coefficients. The results obtained compose a preliminary step towards the study of strong solvability (in Sobolev or Morrey spaces) of boundary value problems for quasilinear elliptic operators with discontinuous coefficients.File in questo prodotto:
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