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تسجيل مستخدم جديدOn a class of divergence form linear parabolic equations with degenerate coefficients
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We study a class of linear parabolic equations in divergence form with degenerate coefficients on the upper half space. Specifically, the equations are considered in $(-infty, T) times mathbb{R}^d_+$, where $mathbb{R}^d_+ = {x in mathbb{R}^d,:, x_d>0}$ and $Tin {(-infty, infty]}$ is given, and the diffusion matrices are the product of $x_d$ and bounded uniformly elliptic matrices, which are degenerate at ${x_d=0}$. As such, our class of equations resembles well the corresponding class of degenerate viscous Hamilton-Jacobi equations. We obtain wellposedness results and regularity type estimates in some appropriate weighted Sobolev spaces for the solutions.
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