We prove an estimate on the $L^2(\Omega)$-norm of the Hessian of a function $u \in W^{2,q}(\Omega)$, satisfying an oblique derivative type condition on the boundary, allowing the oblique axis to be tangential at a finite number of points of $\partial \Omega$. Using this inequality, the solvability in Sobolev spaces $W^{2,q}(\Omega)$, with $q$ closed to $2$, follows for a class of nonlinear differential equations in the plane with quadratic growth.

On an estimate related to the Hessian and application to an oblique derivative problem

GIUFFRE', Sofia
2005-01-01

Abstract

We prove an estimate on the $L^2(\Omega)$-norm of the Hessian of a function $u \in W^{2,q}(\Omega)$, satisfying an oblique derivative type condition on the boundary, allowing the oblique axis to be tangential at a finite number of points of $\partial \Omega$. Using this inequality, the solvability in Sobolev spaces $W^{2,q}(\Omega)$, with $q$ closed to $2$, follows for a class of nonlinear differential equations in the plane with quadratic growth.
2005
Hessian estimate; nonlinear elliptic equations; tangential oblique derivative problem; strong solutions
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12318/3720
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? ND
social impact