Regularity of very weak solutions for elliptic equation of divergence form
نویسندگان
چکیده
منابع مشابه
On the C regularity of solutions to divergence form elliptic systems with Dini-continuous coefficients
We prove C1 regularity of solutions to divergence form elliptic systems with Dini-continuous coefficients. This note addresses a question raised to the author by Haim Brezis, in connection with his solution of a conjecture of Serrin concerning divergence form second order elliptic equations (see [1] and [2]). If the coefficients of the equations (or systems) are Hölder continuous, then H1 solut...
متن کاملBoundary Regularity of Weak Solutions to Nonlinear Elliptic Obstacle Problems
for all v∈ ={v∈W 0 (Ω), v≥ψ a.e. in Ω}. Here Ω is a bounded domain in RN (N≥2) with Lipschitz boundary, 2≤ p ≤N . A(x,ξ) :Ω×RN → RN satisfies the following conditions: (i) A is a vector valued function, the mapping x → A(x,ξ) is measurable for all ξ ∈ RN , ξ → A(x,ξ) is continuous for a.e. x ∈Ω; (ii) the homogeneity condition: A(x, tξ)= t|t|p−2A(x,ξ), t ∈ R, t = 0; (iii) the monotone inequality...
متن کاملRegularity of Weak Solutions to the Monge–ampère Equation
We study the properties of generalized solutions to the Monge– Ampère equation detD2u = ν, where the Borel measure ν satisfies a condition, introduced by Jerison, that is weaker than the doubling property. When ν = f dx, this condition, which we call D , admits the possibility of f vanishing or becoming infinite. Our analysis extends the regularity theory (due to Caffarelli) available when 0 < ...
متن کاملExistence and uniqueness of weak solutions for a class of nonlinear divergence type diffusion equations
In this paper, we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations. By a priori estimates, difference and variation techniques, we establish the existence and uniqueness of weak solutions of this problem.
متن کاملQuasilinear Elliptic Systems in Divergence Form with Weak Monotonicity
We consider the Dirichlet problem for the quasilinear elliptic system − div σ(x, u(x), Du(x)) = f on Ω u(x) = 0 on ∂Ω for a function u : Ω → Rm, where Ω is a bounded open domain in Rn. For arbitrary right hand side f ∈W−1,p (Ω) we prove existence of a weak solution under classical regularity, growth and coercivity conditions, but with only very mild monotonicity assumptions.
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 of Functional Analysis
سال: 2012
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2011.11.027