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1.
One constructs examples of strongly elliptic second-order differential equations in the divergence form with measurable bounded complex coefficients in Rn, n3, whose generalized solutions are not bounded in any neighborhood of the origin.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta, im. V. A. Steklova AN SSSR, Vol. 115, pp. 156–168, 1982. 相似文献
2.
V. G. Maz'ya 《Journal of Mathematical Sciences》1983,22(6):1851-1855
By definition, the domain Ω ??n belongs to the class EW p l if there exists a continuous linear extension operator . An example is given of a domain Ω ??2 with compact closure and Jordan boundary, having the following properties: (1) The curve ?Ω is not a quasicircle, has finite length and is Lipschitz in a neighborhood of any of its points except one. (2) Ω ε EW p 1 for p<2. and Ω ? EW p 1 for p?2. (3) for p>2 and for p?2. 相似文献
3.
In this paper the Agmon-Miranda maximum principle for solutions of strongly elliptic differential equations Lu = 0 in a bounded domain G with a conical point is considered. Necessary and sufficient conditions for the validity of this principle are given both for smooth solutions of the equation Lu = 0 in G and for the generalized solution of the problem Lu = 0 in G, D
k
v
u = gk on G (k = 0,...,m-1). It will be shown that for every elliptic operator L of order 2m > 2 there exists such a cone in n (n4) that the Agmon-Miranda maximum principle fails in this cone. 相似文献
4.
We consider systems of partial differential equations, which contain only second derivatives in the x variables and which are uniformly parabolic in the sense of Petrovskii. For such systems we obtain necessary and, separately, sufficient conditions for the maximum norm principle to hold in the layer Rn × ( 0,T ] and in the cylinder × ( 0,T], where is a bounded subdomain of Rn. In this paper the norm is understood in a generalized sense, i.e. as the Minkowski functional of a compact convex body in Rm containing the origin. The necessary and sufficient conditions coincide if the coefficients of the system do not depend on t. The criteria for validity of the maximum norm principle are formulated as a number of equivalent algebraic conditions describing the relation between the geometry of the unit sphere of the given norm and coefficients of the system under consideration. Simpler formulated criteria are given for certain classes of norms: for differentiable norms, p-norms ( 1 p ) in Rm, as well as for norms whose unit balls are m-pyramids, m-bipyramids, cylindrical bodies, m-parallelepipeds. The case m = 2 is studied separately. 相似文献
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6.
The paper studies quasi-interpolation by scaled shifts of a smooth and rapidly decaying function. The centers are images of a smooth mapping of the hZn-lattice in Rs, sn, and the scaling parameters are proportional to h. We show that for a large class of generating functions the quasi-interpolants provide high order approximations up to some prescribed accuracy. Although in general the approximants do not converge as h tends to zero, the remaining saturation error is negligible in numerical computations if a scalar parameter is suitably chosen. The lack of convergence is compensated for by a greater flexibility in the choice of generating functions used in numerical methods for solving operator equations. 相似文献
7.
Angelo Alvino Andrea Cianchi Vladimir G. Maz'ya Anna Mercaldo 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2010
Non-linear elliptic Neumann problems, possibly in irregular domains and with data affected by low integrability properties, are taken into account. Existence, uniqueness and continuous dependence on the data of generalized solutions are established under a suitable balance between the integrability of the datum and the (ir)regularity of the domain. The latter is described in terms of isocapacitary inequalities. Applications to various classes of domains are also presented. 相似文献
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10.
V. G. Maz'ya 《Journal of Mathematical Sciences》1978,10(1):86-89
Conditions for unique solvability are given for the problem of steady-state oscillations of a body submerged in a heavy ideal fluid.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 69, pp. 124–128, 1977. 相似文献