The cauchy-dirichlet problem for parabolic equations with VMO coefficients
نویسندگان
چکیده
منابع مشابه
Parabolic Equations with Variably Partially Vmo Coefficients
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 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 کاملThe Cauchy-Dirichlet Problem for a Class of Linear Parabolic Differential Equations with Unbounded Coefficients in an Unbounded Domain
Correspondence should be addressed to Gerardo Rubio, [email protected] Received 20 December 2010; Revised 18 March 2011; Accepted 19 April 2011 Academic Editor: Lukasz Stettner Copyright q 2011 Gerardo Rubio. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the origin...
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.
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ژورنال
عنوان ژورنال: Mathematical and Computer Modelling
سال: 2005
ISSN: 0895-7177
DOI: 10.1016/j.mcm.2005.03.004