Gradient Estimates for Solutions to Divergence Form Elliptic Equations with Discontinuous Coefficients
نویسندگان
چکیده
منابع مشابه
Gradient Estimates for Solutions to Divergence Form Elliptic Equations with Discontinuous Coefficients
In this paper we derive globalW 1,∞ and piecewiseC1,α estimates for solutions to divergence form elliptic equations with piecewise Hölder continuous coefficients. The novelty of these estimates is that, even though they depend on the shape and on the size of the surfaces of discontinuity of the coefficients, they are independent of the distance between these surfaces.
متن کاملElliptic Equations in Divergence Form with Partially Bmo Coefficients
The solvability in Sobolev spaces is proved for divergence form second order elliptic equations in the whole space, a half space, and a bounded Lipschitz domain. For equations in the whole space or a half space, the leading coefficients a are assumed to be measurable in one direction and have small BMO semi-norms in the other directions. For equations in a bounded domain, additionally we assume...
متن کاملFundamental Solutions to Some Elliptic Equations with Discontinuous Senior Coefficients and an Inequality for These Solutions
Let Lu := ∇ · (a(x)∇u) = −δ(x − y) in R3 , 0 < c1 a(x) c2 , a(x) is a piecewise-smooth function with the discontinuity surface S which is smooth. It is proved that in an neighborhood of S the behavior of the function u is given by the formula: u(x, y) = ⎧⎨ ⎩ (4πa+)−1[r−1 xy + bR−1], y3 > 0, (4πa−)−1[r−1 xy − bR−1], y3 < 0. ( ∗ ) Here the local coordinate system is chosen in which the origin lie...
متن کاملLorentz estimates for the gradient of weak solutions to elliptic obstacle problems with partially BMO coefficients
We prove global Lorentz estimates for variable power of the gradient of weak solution to linear elliptic obstacle problems with small partially BMO coefficients over a bounded nonsmooth domain. Here, we assume that the leading coefficients are measurable in one variable and have small BMO semi-norms in the other variables, variable exponents p(x) satisfy log-Hölder continuity, and the boundarie...
متن کاملOn 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 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: Archive for Rational Mechanics and Analysis
سال: 2000
ISSN: 0003-9527,1432-0673
DOI: 10.1007/s002050000082