کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
839434 1470475 2015 46 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Harnack’s inequality and Hölder continuity for weak solutions of degenerate quasilinear equations with rough coefficients
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
Harnack’s inequality and Hölder continuity for weak solutions of degenerate quasilinear equations with rough coefficients
چکیده انگلیسی

We continue to study regularity results for weak solutions of the large class of second order degenerate quasilinear equations of the form div(A(x,u,∇u))=B(x,u,∇u)for  x∈Ω as considered in our paper Monticelli et al. (2012). There we proved only local boundedness of weak solutions. Here we derive a version of Harnack’s inequality as well as local Hölder continuity for weak solutions. The possible degeneracy of an equation in the class is expressed in terms of a nonnegative definite quadratic form associated with its principal part. No smoothness is required of either the quadratic form or the coefficients of the equation. Our results extend ones obtained by J. Serrin (1964) and N. Trudinger (1967) for quasilinear equations, as well as ones for subelliptic linear equations obtained in Sawyer and Wheeden (2006, 2010).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 126, October 2015, Pages 69–114
نویسندگان
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