Oblique derivative problem for quasilinear elliptic equations with VMO coefficients
نویسندگان
چکیده
منابع مشابه
Oblique derivative problem for elliptic equations in non-divergence form with VMO coefficients
A priori estimates and strong solvability results in Sobolev space W 2,p(Ω), 1 < p < ∞ are proved for the regular oblique derivative problem 8<: Pni,j=1 aij(x) ∂u ∂xi∂xj = f(x) a.e. Ω ∂u ∂l + σ(x)u = φ(x) on ∂Ω when the principal coefficients aij are VMO ∩ L∞ functions.
متن کاملParabolic and Elliptic Equations with Vmo Coefficients
An Lp-theory of divergence and non-divergence form elliptic and parabolic equations is presented. The main coefficients are supposed to belong to the class V MOx, which, in particular, contains all functions independent of x. Weak uniqueness of the martingale problem associated with such equations is obtained.
متن کاملOptimal Partial Regularity for Quasilinear Elliptic Systems with Vmo Coefficients Based on A-harmonic Approximations
− Dα(A i j (x, u)Dβu j) = Bi(x, u,Du), a. e. x ∈ Ω, i = 1, 2, . . . ,N; (1.1) where A(x, u) = (A i j (x, u)) is a VMO function in x ∈ Ω uniformly with respect to u ∈ RN and continuous in u uniformly with respect to x ∈ Ω, and Bi(x, u,Du) satisfies the controllable growth. In the context, we adopt Einstein’s convention by summing over repeated indices with α, β = 1, 2, . . . , n and i, j = 1, 2,...
متن کاملParabolic and Elliptic Systems with Vmo Coefficients
We consider second order parabolic and elliptic systems with leading coefficients having the property of vanishing mean oscillation (VMO) in the spatial variables. An Lq −Lp theory is established for systems both in divergence and non-divergence form. Higher order parabolic and elliptic systems are also discussed briefly.
متن کاملParabolic Equations with Variably Partially Vmo Coefficients
We prove the W 1,2 p -solvability of second order parabolic equations in nondivergence form in the whole space for p ∈ (1,∞). The leading coefficients are assumed to be measurable in one spatial direction and have vanishing mean oscillation (VMO) in the orthogonal directions and the time variable in each small parabolic cylinder with the direction depending on the cylinder. This extends a recen...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1996
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700017275