Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms
نویسندگان
چکیده
منابع مشابه
Parabolic Equations with Vmo Coefficients in Spaces with Mixed Norms
An Lq(Lp)-theory of divergence and non-divergence form parabolic equations is presented. The main coefficients are supposed to belong to the class V MOx, which, in particular, contains all measurable functions depending only on t. The method of proving simplifies the methods previously used in the case p = q.
متن کاملParabolic Equations with Partially Vmo Coefficients and Boundary Value Problems in Sobolev Spaces with Mixed Norms
Second order parabolic equations in Sobolev spaces with mixed norms are studied. The leading coefficients (except a) are measurable in both time and one spatial variable, and VMO in the other spatial variables. The coefficient a is measurable in time and VMO in the spatial variables. The unique solvability of equations in the whole space is applied to solving Dirichlet and oblique derivative pr...
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We prove the W 1,2 p -solvability of second order parabolic equations in nondivergence form in the whole space for p ∈ (1,∞). The leading coefficients are assumed to be measurable in one spatial direction and have vanishing mean oscillation (VMO) in the orthogonal directions and the time variable in each small parabolic cylinder with the direction depending on the cylinder. This extends a recen...
متن کاملParabolic and Elliptic Equations with Vmo Coefficients
An Lp-theory of divergence and non-divergence form elliptic and parabolic equations is presented. The main coefficients are supposed to belong to the class V MOx, which, in particular, contains all functions independent of x. Weak uniqueness of the martingale problem associated with such equations is obtained.
متن کاملPARABOLIC EQUATIONS WITH MEASURABLE COEFFICIENTS IN Lp-SPACES WITH MIXED NORMS
The unique solvability of parabolic equations in Sobolev spaces with mixed norms is presented. The second order coefficients (except a) are assumed to be only measurable in time and one spatial variable, and VMO in the other spatial variables. The coefficient a is measurable in one spatial variable and VMO in the other variables.
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2007
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2007.04.003