Results 31 to 40 of about 444 (158)
Parabolic and Elliptic Equations with VMO Coefficients [PDF]
Communications in Partial Differential Equations, 2007 An $L_{p}$-theory of divergence and non-divergence form elliptic and parabolic equations is presented. The main coefficients are supposed to belong to the class $VMO_{x}$, which, in particular, contains all functions independent of $x$. Weak uniqueness of the martingale problem associated with such equations is obtained.
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Regularity results for singular elliptic problems
Journal of Function Spaces and Applications, 2006 Some local and global regularity results for solutions of linear elliptic equations in weighted spaces are proved. Here the leading coefficients are VMO functions, while the hypotheses on the other coefficients and the boundary conditions involve a ...
Loredana Caso
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The Dirichlet Problem for elliptic equations in unbounded domains of the plane
Journal of Function Spaces and Applications, 2008 In this paper we prove a uniqueness and existence theorem for the Dirichlet problem in W2,p for second order linear elliptic equations in unbounded domains of the plane.
Paola Cavaliere, Maria Transirico
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Quasilinear elliptic equations with VMO coefficients [PDF]
Transactions of the American Mathematical Society, 1995 Strong solvability and uniqueness in Sobolev space W 2
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Partial regularity for parabolic systems with VMO-coefficients
Communications on Pure and Applied Analysis, 2021 The author studies the regularity properties of the solutions of the following parabolic system in divergence form \[ u_t-\mathrm{div} A(x,t,u,Du)=0 \qquad \text{ in } \Omega_T=\Omega\times(-T,0)) \] It is established a partial Hölder regularity result for the weak solutions imposing standard \(p\)-growth condition and ellipticity condition on the ...
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An alternative approach to partial regularity of quasilinear elliptic systems with VMO coefficients
Journal of Inequalities and Applications, 2016 In this paper, we provide an alternative approach to partially Hölder continuity of some quasilinear elliptic systems with discontinuous coefficients under natural growth.
Haiyan Yu, Shenzhou Zheng, Yuxia Tong
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Parabolic equations with variably partially VMO coefficients [PDF]
St. Petersburg Mathematical Journal, 2012 We prove the $W^{1,2}_{p}$-solvability of second order parabolic equations in nondivergence form in the whole space for $p\in (1,\infty)$. 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 ...
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W2,p a priori estimates for nonvariational operators: the sharp maximal function technique
Bruno Pini Mathematical Analysis Seminar, 2018 We consider a nonvariational degenerate elliptic operator, structured on a system of left invariant, 1-homogeneous, Hörmander vector fields on a Carnot group, where the coefficient matrix is symmetric, uniformly positive on a bounded domain and the ...
Marco Bramanti
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Open Mathematics, 2016 We obtain the global weighted Morrey-type regularity of the solution of the regular oblique derivative problem for linear uniformly parabolic operators with VMO coefficients.
Guliyev Vagif S., Omarova Mehriban N.
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PARTIAL REGULARITY OF THE MINIMIZERS OF QUADRATIC FUNCTIONALS WITH VMO COEFFICIENTS
Journal of the London Mathematical Society, 2005 Summary: The paper investigates the partial regularity of the minimizers for quadratic functionals whose integrands have VMO coefficients in principal part and nonlinear terms that are Carathéodory functions. We use some majorizations for the functional, rather than the well known Euler equation associated to it.
RAGUSA, Maria Alessandra +1 more
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