Dirichlet problem for semilinear edge-degenerate elliptic equations with singular potential term
نویسندگان
چکیده
منابع مشابه
The 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 کاملSingular Solutions for some Semilinear Elliptic Equations
We are concerned with the behavior of u near x = O. There are two distinct cases: 1) When p >= N / ( N -2) and (N ~ 3) it has been shown by BR~ZIS & V~RON [9] that u must be smooth at 0 (See also BARAS & PIERRE [1] for a different proof). In other words, isolated singularities are removable. 2) When 1-< p < N / ( N 2) there are solutions of (1) with a singularity at x ---0. Moreover all singula...
متن کاملDegenerate elliptic equations with singular nonlinearities
The behavior of the “minimal branch” is investigated for quasilinear eigenvalue problems involving the p-Laplace operator, considered in a smooth bounded domain of RN , and compactness holds below a critical dimension N #. The nonlinearity f (u) lies in a very general class and the results we present are new even for p = 2. Due to the degeneracy of p-Laplace operator, for p = 2 it is crucial to...
متن کاملOn a singular nonlinear semilinear elliptic problem
where K(x)μC2,b(V9 ), a, pμ(0, 1) and l is a real parameter. Such singular elliptic problems arise in the contexts of chemical heterogeneous catalysts, nonNewtonian fluids and also the theory of heat conduction in electrically conducting materials, see [3, 5, 8, 9] for a detailed discussion. Obviously (1.1) cannot have a solution uμC2(V9 ) if K(x) is not vanishing near ∂V. However, under variou...
متن کاملExistence Results for a Class of Semilinear Degenerate Elliptic Equations
We prove existence results for the Dirichlet problem associated with an elliptic semilinear second-order equation of divergence form. Degeneracy in the ellipticity condition is allowed.
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 Differential Equations
سال: 2012
ISSN: 0022-0396
DOI: 10.1016/j.jde.2012.01.011