A note on polynomial approximation in Sobolev spaces
Rüdiger Verfürth (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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For domains which are star-shaped w.r.t. at least one point, we give new bounds on the constants in Jackson-inequalities in Sobolev spaces. For convex domains, these bounds do not depend on the eccentricity. For non-convex domains with a re-entrant corner, the bounds are uniform w.r.t. the exterior angle. The main tool is a new projection operator onto the space of polynomials.