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Pré-Publication, Document De Travail Année : 2014

Local solvability of the $k$-Hessian equations

Résumé

In this work, we study the existence of local solutions in $\mathbb{R}^{n}$ to $k$-Hessian equation,for which the nonhomogeneous term $f$ is permitted to change the sign or be non negative; if $f$ is $C^\infty,$ so is the local solution. We also give a classification for the second order polynomial solutions to the $k-$Hessian equation, it is the basis to construct the local solutions and obtain the uniform ellipticity of the linearized operators at such constructed local solutions.
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Dates et versions

hal-01093001 , version 1 (09-12-2014)
hal-01093001 , version 2 (14-12-2014)

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G Tian, Qi Wang, C.-J Xu. Local solvability of the $k$-Hessian equations. 2014. ⟨hal-01093001v2⟩
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