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

The Best Writing on Mathematics 2012

This annual anthology brings jointly the year's most interesting arithmetic writing from worldwide. that includes promising new voices along a number of the most excellent names within the box, the simplest Writing on arithmetic 2012 makes to be had to a large viewers many articles no longer simply came upon wherever else--and you don't have to be a mathematician to get pleasure from them.

The Life of William Thomson-Baron Kelvin of Largs

It is a pre-1923 historic copy that was once curated for caliber. caliber insurance used to be performed on every one of those books in an try and get rid of books with imperfections brought through the digitization technique. even though we now have made most sensible efforts - the books can have occasional blunders that don't bog down the interpreting adventure.

Computer mathematics : proceedings of the Sixth Asian Symposium (ASCM 2003), Beijing, China, 17-19 April 2003

Released in honour of Professor Gu Chaohao, this paintings covers matters heavily with regards to differential geometry, partial differential equations and mathematical physics, the main parts within which Professor Gu has obtained outstanding achievements at the department of Generalized Polynomials (N Aris & A Rahman); On One estate of Hurwitz Determinants (L Burlakova); mixing Quadric Surfaces through a Base Curve procedure (J Cheng); An Exploration of Homotopy fixing in Maple (K Hazaveh et al.

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

Sample text

23 page 23 October 12, 2015 10:9 24 9108 - Differential Geometry from a Singularity Theory Viewpoint 9789814590440 Differential Geometry from a Singularity Theory Viewpoint Let u = (u1 , . . , un ) denote the coordinates of a point in U with respect to the canonical basis of Rn . The tangent space Tp M of M at p = x(u) is an n-dimensional vector space generated by the linearly independent vectors of the partial derivatives of x at u. We take these vectors as a basis B(x) of Tp M , so B(x) = {xu1 (u), .

We have Nui (u) = −κ(u)xui (u), i = 1, . . , n, so for i, j = 1, . . , n, Nui uj (u) = −κuj (u)xui (u) − κ(u)xui uj (u). 3) The maps x and N are C ∞ -maps, therefore Nui uj (u) − Nuj ui (u) = 0 and xui uj (u) − xuj ui (u) = 0 for i, j = 1, . . , n. 3) that κuj (u)xui (u) − κui (u)xuj (u) = 0 for i, j = 1, . . , n. However, the vectors xu1 (u), . . , xun (u) are linearly independent, so κui (u) = 0 for i = 1, . . , n, that is, κ(u) is a constant function κ. We have two possibilities depending on whether κ is zero or not.

Furthermore, we have r βik = r βi δ k = =1 βi ν k , ν = νk , Gνui = νk , νui . =1 We have, from the definition of the coefficients of the ν-second fundamental form, s −hνi = νui , xu = Gνui , xu s αij xuj , xu = j=1 αij gj . = j=1 Thus, (αij ) = −(hνi )(g j )−1 = −(hji )ν . The expression for (π T ◦ Gν )ui follows from the fact that the vectors νi (u) are normal vectors. 3. The Lipschitz-Killing curvature of M at p = x(u) along the unit normal vector field ν is given by K ν (u) = det(hνij (u)) .

Download PDF sample

Rated 4.69 of 5 – based on 27 votes