We prove Lloc∞ estimates for positive solutions to the following degenerate second order partial differential equation of Kolmogorov type with measurable coefficients of the form ∑i,j=1m0∂xjavax.xml.bind.JAXBElement@14c7905daij(x,t)∂xjavax.xml.bind.JAXBElement@41a3b5feu(x,t)+∑i,j=1Nbijxj∂xjavax.xml.bind.JAXBElement@21dceba6u(x,t)−∂tu(x,t)++∑i=1m0bi(x,t)∂iu(x,t)−∑i=1m0∂xjavax.xml.bind.JAXBElement@638b72d3ai(x,t)u(x,t)+c(x,t)u(x,t)=0 where (x,t)=(x1,…,xN,t)=z is a point of RN+1, and 1≤m0≤N. (aij) is a uniformly positive symmetric matrix with bounded measurable coefficients, (bij) is a constant matrix. We apply the Moser's iteration method to prove the local boundedness of the solution u under minimal integrability assumption on the coefficients.

Moser's estimates for degenerate Kolmogorov equations with non-negative divergence lower order coefficients / Anceschi, F.; Polidoro, S.; Ragusa, M. A.. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 189:(2019), pp. 1-19. [10.1016/j.na.2019.07.001]

Moser's estimates for degenerate Kolmogorov equations with non-negative divergence lower order coefficients

Anceschi F.
Membro del Collaboration Group
;
Polidoro S.
Membro del Collaboration Group
;
2019

Abstract

We prove Lloc∞ estimates for positive solutions to the following degenerate second order partial differential equation of Kolmogorov type with measurable coefficients of the form ∑i,j=1m0∂xjavax.xml.bind.JAXBElement@14c7905daij(x,t)∂xjavax.xml.bind.JAXBElement@41a3b5feu(x,t)+∑i,j=1Nbijxj∂xjavax.xml.bind.JAXBElement@21dceba6u(x,t)−∂tu(x,t)++∑i=1m0bi(x,t)∂iu(x,t)−∑i=1m0∂xjavax.xml.bind.JAXBElement@638b72d3ai(x,t)u(x,t)+c(x,t)u(x,t)=0 where (x,t)=(x1,…,xN,t)=z is a point of RN+1, and 1≤m0≤N. (aij) is a uniformly positive symmetric matrix with bounded measurable coefficients, (bij) is a constant matrix. We apply the Moser's iteration method to prove the local boundedness of the solution u under minimal integrability assumption on the coefficients.
2019
16-lug-2019
189
1
19
Moser's estimates for degenerate Kolmogorov equations with non-negative divergence lower order coefficients / Anceschi, F.; Polidoro, S.; Ragusa, M. A.. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 189:(2019), pp. 1-19. [10.1016/j.na.2019.07.001]
Anceschi, F.; Polidoro, S.; Ragusa, M. A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1179479
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