Journal article
KRYLOV'S BOUNDARY GRADIENT TYPE ESTIMATES FOR SOLUTIONS TO FULLY NONLINEAR DIFFERENTIAL INEQUALITIES WITH QUADRATIC GROWTH ON THE GRADIENT
SIAM journal on mathematical analysis, Vol.52(5), pp.4469-4505
01/01/2020
DOI: 10.1137/19M1262863
Abstract
In this paper we prove Krylov's boundary gradient type estimates (and regularity) for solutions to fully nonlinear differential inequalities with unbounded coefficients and quadratic growth on the gradient with C-1,C-dini boundary data. This means that drift coefficients and the right-hand side (RHS) are in L-q with q > n. We also show that in the case the RHS is in L' the result does not hold and solutions may fail to be even Lipschitz in (tiny) neighborhoods of the boundary. Our approach is based on a new improvement of flatness argument together with an iteration process based on scaling arguments and perturbation by linear functions. Our results can be seen as an extension of the corresponding ones obtained in [L. Silvestre and B. Sirakov, Comm. Partial Differential Equations, 39 (2014), pp. 1694-1717] in the case of bounded coefficients and no quadratic term.
Details
- Title: Subtitle
- KRYLOV'S BOUNDARY GRADIENT TYPE ESTIMATES FOR SOLUTIONS TO FULLY NONLINEAR DIFFERENTIAL INEQUALITIES WITH QUADRATIC GROWTH ON THE GRADIENT
- Creators
- J. Ederson M Braga - Univ Fed Ceara, Dept Matemat, Campus Pici,Bloco 914, BR-60455760 Fortaleza, Ceara, BrazilDiego E. M Gomes - Instituto Federal de Educação, Ciência e Tecnologia do CearáDiego Moreira - Univ Fed Ceara, Dept Matemat, Campus Pici,Bloco 914, BR-60455760 Fortaleza, Ceara, BrazilLihe Wang - Univ Iowa, Dept Math, Iowa City, IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- SIAM journal on mathematical analysis, Vol.52(5), pp.4469-4505
- DOI
- 10.1137/19M1262863
- ISSN
- 0036-1410
- eISSN
- 1095-7154
- Publisher
- SIAM PUBLICATIONS
- Number of pages
- 37
- Grant note
- FUNCAP (PRONEX) CNPq (Brazil); Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPQ)
- Language
- English
- Date published
- 01/01/2020
- Academic Unit
- Mathematics
- Record Identifier
- 9984240874502771
Metrics
24 Record Views