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Partial Gaussian Bounds for Degenerate Differential Operators
Language
en
Article de revue
This item was published in
Potential Analysis. 2011, vol. 35, n° 2, p. 175-199
Springer Verlag
English Abstract
Let S be the semigroup on L2(Rd) generated by a degenerate elliptic operator, formally equal to − ∂k ckl ∂l , where the coefficients ckl are real bounded measurable and the matrix C(x) = (ckl(x)) is symmetric and positive ...Read more >
Let S be the semigroup on L2(Rd) generated by a degenerate elliptic operator, formally equal to − ∂k ckl ∂l , where the coefficients ckl are real bounded measurable and the matrix C(x) = (ckl(x)) is symmetric and positive semi-definite for all x ∈ Rd. Let ⊂ Rd be a bounded Lipschitz domain and μ > 0. Suppose that C(x) ≥ μ I for all x ∈ . We show that the operator P St P has a kernel satisfying Gaussian bounds and Gaussian Hölder bounds, where P is the projection of L2(Rd) onto L2( ). Similar results are for the operators u → χ St(χ u), where χ ∈ C∞ b (Rd) and C(x) ≥ μI for all x ∈ supp χ.Read less <
English Keywords
Degenerate operators
Gaussian bounds
Morrey and Campanato spaces
Origin
Hal imported