Local solvability in LP of first order semilinear equations

1996 ◽  
Vol 10 (7) ◽  
Author(s):  
Jorge Hounie ◽  
Paulo Santiago
Keyword(s):  
Local Solvability ◽  
Semilinear Equations ◽  
First Order

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

2006 ◽  
Vol 99 (2) ◽  
pp. 175 ◽  
Author(s):  
David Jornet ◽  
Alessandro Oliaro
Keyword(s):  
Fourier Transform ◽  
Smooth Function ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Local Solvability ◽  
Functional Composition ◽  
Fully Nonlinear Elliptic Equations ◽  
Semilinear Equations ◽  
Nonlinear Elliptic ◽  
Good Behaviour

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.

On the local solvability of semilinear equations

1995 ◽  
Vol 20 (9-10) ◽  
pp. 1777-1789 ◽  
Author(s):  
Jorge Hounie ◽  
Paulo Santiago
Keyword(s):  
Local Solvability ◽  
Semilinear Equations
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