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We give sufficient conditions under which solutions of discretized in space second-order parabolic and elliptic equations, perhaps degenerate, admit estimates of the first derivatives in the space variables independent of the mesh size.<\/p>","DOI":"10.1090\/s0025-5718-09-02229-7","type":"journal-article","created":{"date-parts":[[2009,6,30]],"date-time":"2009-06-30T14:39:02Z","timestamp":1246372742000},"page":"2019-2046","source":"Crossref","is-referenced-by-count":3,"title":["First derivatives estimates for finite-difference schemes"],"prefix":"10.1090","volume":"78","author":[{"given":"Istv\u00e1n","family":"Gy\u00f6ngy","sequence":"first","affiliation":[]},{"given":"Nicolai","family":"Krylov","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1090\/S1061-0022-06-00905-8","article-title":"On the rate of convergence of finite-difference approximations for Bellman equations with constant coefficients","volume":"17","author":"Dong, Hongjie","year":"2005","journal-title":"Algebra i Analiz","ISSN":"http:\/\/id.crossref.org\/issn\/0234-0852","issn-type":"print"},{"key":"2","first-page":"No. 102, 25","article-title":"Rate of convergence of finite-difference approximations for degenerate linear parabolic equations with \ud835\udc36\u00b9 and \ud835\udc36\u00b2 coefficients","author":"Dong, Hongjie","year":"2005","journal-title":"Electron. 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