کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4590113 1334934 2014 41 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Subdifferential calculus and doubly nonlinear evolution equations in LpLp-spaces with variable exponents
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Subdifferential calculus and doubly nonlinear evolution equations in LpLp-spaces with variable exponents
چکیده انگلیسی

This paper is concerned with the Cauchy–Dirichlet problem for a doubly nonlinear parabolic equation involving variable exponents and provides some theorems on existence and regularity of strong solutions. In the proof of these results, we also analyze the relations occurring between Lebesgue spaces of space–time variables and Lebesgue–Bochner spaces of vector-valued functions, with a special emphasis on measurability issues and particularly referring to the case of space-dependent variable exponents. Moreover, we establish a chain rule for (possibly nonsmooth) convex functionals defined on variable exponent spaces. Actually, in such a peculiar functional setting the proof of this integration formula is nontrivial and requires a proper reformulation of some basic concepts of convex analysis, like those of resolvent, of Yosida approximation, and of Moreau–Yosida regularization.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 267, Issue 1, 1 July 2014, Pages 173–213
نویسندگان
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