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mathcal W^(α, p) and C^(0,γ) regularity of solutions to (μ - Delta + b cdot nabla)u=f with form-bounded vector fields
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$\mathcal W^{\alpha, p}$ and $C^{0,\gamma}$ regularity of solutions to $(\mu - \Delta + b \cdot \nabla)u=f$ with form-bounded vector fields
abstract
We consider the operator $-\Delta +b \cdot \nabla$ with $b:\mathbb R^d \rightarrow \mathbb R^d$ ($d \geq 3$) in the class of form-bounded vector fields (containing vector fields having critical-order singularities), and characterize quantitative dependence of the $\mathcal W^{1+\frac{2}{q},p}$ ($2 \leq p < q$) and the $C^{0,\gamma}$ regularity of solutions to the corresponding elliptic equation in $L^p$ on the value of the form-bound of $b$.
Forward citations
Cited by 2 Pith papers
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