Functional composition in $B_{p,k}$ spaces and applications

Authors

  • David Jornet
  • Alessandro Oliaro

DOI:

https://doi.org/10.7146/math.scand.a-15008

Abstract

Let $f(x,z)$, $x\in\mathsf{R}^N$, $z\in \mathsf{C}^M$, be a smooth function in the sense that its Fourier transform has a good behaviour. We study the composition $f(x,u(x))$, where $u$ is in a generalized Hörmander $B_{p,k}$ space in the sense of Björck [1]. As a consequence we obtain results of local solvability and hypoellipticity of semilinear equations of the type $P(D)u+f(x,Q_1(D)u,\ldots,Q_M(D)u)=g$, with $g\in B_{p,k}$, and fully nonlinear elliptic equations.

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Published

2006-12-01

How to Cite

Jornet, D., & Oliaro, A. (2006). Functional composition in $B_{p,k}$ spaces and applications. MATHEMATICA SCANDINAVICA, 99(2), 175–203. https://doi.org/10.7146/math.scand.a-15008

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Section

Articles