On Divergence Form Spdes with Vmo Coefficients in a Half Space
نویسنده
چکیده
We extend several known results on solvability in the Sobolev spaces W 1 p , p ∈ [2,∞), of SPDEs in divergence form in R d + to equations having coefficients which are discontinuous in the space variable.
منابع مشابه
On Divergence Form SPDEs with VMO Coefficients
We present several results on solvability in Sobolev spaces W 1 p of SPDEs in divergence form in the whole space.
متن کاملSpdes in Divergence Form with Vmo Coefficients and Filtering Theory of Partially Observable Diffusion Processes with Lipschitz Coefficients
We present several results on the smoothness in Lp sense of filtering densities under the Lipschitz continuity assumption on the coefficients of a partially observable diffusion processes. We obtain them by rewriting in divergence form filtering equation which are usually considered in terms of formally adjoint to operators in nondivergence form.
متن کاملOblique 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 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 کاملOn Divergence Form Spdes with Growing
We consider divergence form uniformly parabolic SPDEs with bounded and measurable leading coefficients and possibly growing lower-order coefficients in the deterministic part of the equations. We look for solutions which are summable to the second power with respect to the usual Lebesgue measure along with their first derivatives with respect to the spatial variable.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008