Regularity of the Dirichlet Problem for Elliptic Equations with Singular Drift
نویسندگان
چکیده
is a Carleson measure in a Lipschitz domain Ω ⊂ R, n ≥ 1, (here δ (X) = dist (X,∂Ω)). If the harmonic measure dωL0 ∈ A∞, then dωL1 ∈ A∞. This is an analog to Theorem 2.17 in [8] for divergence form operators. As an application of this, a new approximation argument and known results we are able to extend the results in [10] for divergence form operators while obtaining totally new results for nondivergence form operators. The theorems are sharp in all cases.
منابع مشابه
Existence Results for a Dirichlet Quasilinear Elliptic Problem
In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.
متن کاملBoundary value problems for elliptic operators with singular drift terms
Let Ω be a Lipschitz domain in R, n ≥ 3, and L = divA∇ − B∇ be a second order elliptic operator in divergence form with real coefficients such that A is a bounded elliptic matrix and the vector field B ∈ Lloc(Ω) is divergence free and satisfies the growth condition dist(X, ∂Ω)|B(X)| ≤ ε1 for ε1 small in a neighbourhood of ∂Ω. For these elliptic operators we will study on the basis of the theory...
متن کاملAnalytic solutions for the Stephen's inverse problem with local boundary conditions including Elliptic and hyperbolic equations
In this paper, two inverse problems of Stephen kind with local (Dirichlet) boundary conditions are investigated. In the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. For the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...
متن کاملThe Dirichlet Problem for Elliptic Equations in Divergence and Nondivergence Form with Singular Drift Term
is a Carleson measure in a Lipschitz domain Ω ⊂ R, n ≥ 1, (here δ (X) = dist (X, ∂Ω)). If the harmonic measure dωL0 ∈ A∞, then dωL1 ∈ A∞. This is an analog to Theorem 2.17 in [8] for divergence form operators. As an application of this, a new approximation argument and known results we obtain: Let L be an elliptic operator with coefficients A and drift term b; L can be in divergence or nondiver...
متن کاملThe Dirichlet Problem for Elliptic Equations with Drift Terms
We establish absolute continuity of the elliptic measure associated to certain second order elliptic equations in either divergence or nondivergence form, with drift terms, under minimal smoothness assumptions on the coefficients.
متن کامل