A note on regularity of solutions to degenerate elliptic by Felli V., Schneider S.

By Felli V., Schneider S.

Show description

Read or Download A note on regularity of solutions to degenerate elliptic equations of Caffarelli-Kohn-Nirenberg type PDF

Best mathematics books

Calculus for the Practical Man (2nd Edition)

This can be the quantity on calculus from the 'Mathematics for self-study' sequence through J E Thompson. It was once initially released in 1931.

Selected papers of P.D. Lax

A well known mathematician who considers himself either utilized and theoretical in his process, Peter Lax has spent so much of his expert profession at NYU, making major contributions to either arithmetic and computing. He has written a number of vital released works and has obtained a variety of honors together with the nationwide Medal of technology, the Lester R.

Discrete Mathematics in Statistical Physics: Introductory Lectures

The publication first describes connections among a few easy difficulties and technics of combinatorics and statistical physics. The discrete arithmetic and physics terminology are with regards to one another. utilizing the validated connections, a few intriguing actions in a single box are proven from a point of view of the opposite box.

Additional info for A note on regularity of solutions to degenerate elliptic equations of Caffarelli-Kohn-Nirenberg type

Sample text

XN(tM)}, {tb ... ,tM} c I, is given and satisfies conditions (a) and (b) of consistency and symmetry stated earlier. 1 The Hilbert Space L2 (11) We are concerned with an important class of stochastic processes called second-order processes. The Hilbert space L2 (Q) occupies a central place in the discussion of properties associated with second-order stochastic processes. Hence, some preliminary remarks concerning the space L2 (Q) are in order. Let {Q, d, P} be a probability space and let X : Q ~ lB.

N}, the increments of Won [ti> ti+1), i = 1, 2, ... n, defined as are independent. , the trajectories of Ware continuous mappings of I into JR with probability one. In other words, at each fixed OJ E Q outside a set of probability zero, the function W (t, OJ) is continuous in tEl. d) EW(t) = 0, tEl. e) The increments {W(s) - W(t)} of Ware stationary in the sense that the expectation E {W(s) - W(t)}2 = IIW(s) - W(t)112 is a function of (s - t) only. ; 0 is an arbitrary constant. 79). A number of interesting properties of the standard Wiener-Levy process can be deduced from these conditions.

S. s. convergent if and only if it is a Cauchy sequence. s. 62) IE {XY}I ~ IIXIIIIYII and note the following useful properties. A) If Xn ~ X, then Ilxnll ~ IIXII and EXn ~ EX. 67), o Continuity of Inner Product. If Xn ~ X and Y m ~ Y as 00, then E{XnYm} ~ E{XY}. This result follows from Cauchy's inequality since B) n, m ~ + IE {Xn (Y - Ym)}1 IIx - XnllllYl1 + IIXnllllY - Ymll , IE {XY} - E {Xn Ym}1 ~ IE {(X - Xn) Y}I ~ which approaches zero as Ilxnll ~ Ilxll < 00 by virtue of (A). s. convergence.

Download PDF sample

Rated 4.64 of 5 – based on 49 votes