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A boundary estimate for non-negative solutions to Kolmogorov operators in non-divergence form
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2012 (English)In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 191, no 1, 1-23 p.Article in journal (Refereed) Published
Abstract [en]

We consider non-negative solutions to a class of second-order degenerate Kolmogorov operators of the form \fancyscriptL=∑i,j=1mai,j(z)∂xixj+∑i=1mai(z)∂xi+∑i,j=1Nbi,jxi∂xj−∂t, where z = (x, t) belongs to an open set Ω⊂RN×R , and 1 ≤ m ≤ N. Let z˜∈Ω , let K be a compact subset of Ω−− , and let Σ⊂∂Ω be such that K∩∂Ω⊂Σ . We give sufficient geometric conditions for the validity of the following Carleson type estimate. There exists a positive constant C K , depending only on Ω,Σ,K,z˜ and on \fancyscriptL , such that supKu≤CKu(z˜), for every non-negative solution u of \fancyscriptLu=0 in Ω such that u∣Σ=0 .

Place, publisher, year, edition, pages
2012. Vol. 191, no 1, 1-23 p.
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URN: urn:nbn:se:uu:diva-163509DOI: 10.1007/s10231-010-0172-zOAI: diva2:464198
Available from: 2011-12-13 Created: 2011-12-12 Last updated: 2013-07-04Bibliographically approved

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Nyström, Kaj
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