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تسجيل مستخدم جديدDegenerate linear parabolic equations in divergence form on the upper half space
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We study a class of second-order degenerate linear parabolic equations in divergence form in $(-infty, T) times mathbb R^d_+$ with homogeneous Dirichlet boundary condition on $(-infty, T) times partial mathbb R^d_+$, where $mathbb R^d_+ = {x in mathbb R^d,:, x_d>0}$ and $Tin {(-infty, infty]}$ is given. The coefficient matrices of the equations are the product of $mu(x_d)$ and bounded uniformly elliptic matrices, where $mu(x_d)$ behaves like $x_d^alpha$ for some given $alpha in (0,2)$, which are degenerate on the boundary ${x_d=0}$ of the domain. Under a partially VMO assumption on the coefficients, we obtain the wellposedness and regularity of solutions in weighted Sobolev spaces. Our results can be readily extended to systems.
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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
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