Local solvability of the k-Hessian equations

الأصل · EN

In this work, we study the existence of local solutions in Rⁿ to k-Hessian equation,for which the nonhomogeneous term f is permitted to change the sign or be non negative; if f is C∞, 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.