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(the second integral is over the boundary hypersurface). This result gives lower bounds for the Dirichlet integral Ja y'2 du, which can be used, for example, in estimation of capacitance. In this… Continue Reading
AbstractConsider a class of functionsY, U on a multidimensional domainA, satisfying a differential equationY′=h(x, Y, U) and given restrictions on values. We seek good lower bounds for a multiple… Continue Reading
Consider a sequence of extensionsIn of a real-valued functionI. Sufficient conditions for the convergence of the infimum ofIn to the infimum ofI are obtained. These conditions are applied to an… Continue Reading
where A is a space of any dimension, ,u a general measure function on a a-algebra of subsets of A, where p(w): A -+ E, o(w): A -+ F are any two maps, and f any scalar function defined on E x F. The… Continue Reading
Multi-valued operators and boundary value problems.- Functional differential equations.- The fourier integral and the expansion problem for ordinary differential operators.- Small solutions of a high… Continue Reading