The anisotropic Cahn–Hilliard equation: Regularity theory and strict separation properties
نویسندگان
چکیده
The Cahn–Hilliard equation with anisotropic energy contributions frequently appears in many physical systems. Systematic analytical results for the case relevant logarithmic free have been missing so far. We close this gap and show existence, uniqueness, regularity, separation properties of weak solutions to energy. Since firstly, becomes highly non-linear, secondly, anisotropies are non-smooth, analysis quite involved. In particular, new regularity quasilinear elliptic equations second order need be shown.
منابع مشابه
On the separation of regularity properties of the reals
We present a model where ω1 is inaccessible by reals, Silver measurability holds for all sets but Miller and Lebesgue measurability fail for some sets. This contributes to a line of research started by Shelah in the 1980s and more recently continued by Schrittesser and Friedman (see [7]), regarding the separation of different notions of regularity properties of the real line. Acknowledgement. T...
متن کاملthe analysis of the role of the speech acts theory in translating and dubbing hollywood films
از محوری ترین اثراتی که یک فیلم سینمایی ایجاد می کند دیالوگ هایی است که هنرپیش گان فیلم میگویند. به زعم یک فیلم ساز, یک شیوه متأثر نمودن مخاطب از اثر منظوره نیروی گفتارهای گوینده, مثل نیروی عاطفی, ترس آور, غم انگیز, هیجان انگیز و غیره, است. این مطالعه به بررسی این مسأله مبادرت کرده است که آیا نیروی فراگفتاری هنرپیش گان به مثابه ی اعمال گفتاری در پنج فیلم هالیوودی در نسخه های دوبله شده باز تولید...
15 صفحه اولOn the Local Regularity of the Kp-i Equation in Anisotropic Sobolev Space
We prove that the KP-I initial-value problem { ∂tu+ ∂ 3 xu− ∂ x ∂ yu+ ∂x(u/2) = 0 on Rx,y × Rt; u(x, y, 0) = φ(x, y), is locally well-posed in the space H(R) = {φ ∈ L(R) : ‖φ‖H1,0(R2) ≈ ‖φ‖L2 + ‖∂xφ‖L2 < ∞}.
متن کاملA stable test for strict sign regularity
A stable test to check if a given matrix is strictly sign regular is provided. Among other nice properties, we prove that it has an optimal growth factor. The test is compared with other alternative tests appearing in the literature, and its advantages are shown.
متن کاملLipschitz regularity for minima without strict convexity of the Lagrangian
We give, in a non-smooth setting, some conditions under which (some of) the minimizers of ∫ Ω f (∇u(x)) dx + g(x,u(x)) dx among the functions in W1,1(Ω) that lie between two Lipschitz functions are Lipschitz. We weaken the usual strict convexity assumption in showing that, if just the faces of the epigraph of a convex function f :Rn → R are bounded and the boundary datum u0 satisfies a generali...
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: Discrete and Continuous Dynamical Systems - Series S
سال: 2023
ISSN: ['1937-1632', '1937-1179']
DOI: https://doi.org/10.3934/dcdss.2023146