Boundary higher integrability for very weak solutions of quasilinear parabolic equations
نویسندگان
چکیده
منابع مشابه
Higher Integrability for Weak Solutions of Higher Order Degenerate Parabolic Systems
We consider a class of higher order nonlinear degenerate parabolic systems, whose easiest model is the parabolic p-Laplacean system ∫ ΩT ( u · φt − |Dmu|p−2Dmu ·Dmφ ) dz = ∫
متن کاملStability of Solutions of Quasilinear Parabolic Equations
Abstract. We bound the difference between solutions u and v of ut = a∆u+ divx f + h and vt = b∆v + divx g + k with initial data φ and ψ, respectively, by ‖u(t, ·)− v(t, ·)‖Lp(E) ≤ AE(t)‖φ−ψ‖ 2ρp L∞(Rn) +B(t)(‖a− b‖∞ + ‖∇x · f − ∇x · g‖∞ + ‖fu − gu‖∞ + ‖h− k‖∞)p |E| ηp . Here all functions a, f , and h are smooth and bounded, and may depend on u, x ∈ R, and t. The functions a and h may in additi...
متن کاملTime-periodic Solutions of Quasilinear Parabolic Differential Equations Ii. Oblique Derivative Boundary Conditions
We study boundary value problems for quasilinear parabolic equations when the initial condition is replaced by periodicity in the time variable. Our approach is to relate the theory of such problems to the classical theory for initial-boundary value problems. In the process, we generalize many previously known results.
متن کاملBoundary Behavior of Solutions of Parabolic Equations
A boundary backward Harnack inequality is proved for positive solutions of second order parabolic equations in non-divergence form in a bounded cylinder Q = (0; T) which vanish on @ x Q = @ (0; T) ; where is a bounded Lipschitz domain in R n. This inequality is applied to the proof of the HH older continuity of the quotient of two positive solutions vanishing on a portion of @ x Q: 1. Introduct...
متن کاملWeak Solutions for a Class of Parabolic Volterra Integrodifferential Equations
u’(t)+Au(t)= ‘a(t,s)g(s,u(s))ds+f(t,U(t)), I 120, 0 u(0) = 0. The operator A is the negative infinitesimal generator of an analytic semigroup in a Banach space X. The operator g(t, u) is related to A by a special form g(t, a) = A”*q(t, u), where q(t, u) is an appropriate “lower order” operator. We show the existence and uniqueness of weak solutions and their continuability to infinity under sui...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 2019
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2018.06.005