On Divergence Form SPDEs with VMO Coefficients
نویسندگان
چکیده
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.
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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.
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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.
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ژورنال
عنوان ژورنال: SIAM Journal on Mathematical Analysis
سال: 2009
ISSN: 0036-1410,1095-7154
DOI: 10.1137/080726902