The Role of Oscillations in Some Nonlinear Problems
Yves Meyer · Birkhäuser Basel eBooks · 2001
The still image compression standard which is being developed under the name of JPEG-2000 (Section 2) is a technological challenge which relies on some advances in pure mathematics. This interaction between image processing and functional analysis also benefits partial differential equations. Indeed new estimates on wavelet coefficients of functions with bounded variation (Theorems 6.6 and 7.5) imply new Gagliardo-Nirenberg inequalities (Section 7) and lead to a better understanding of blowup phenomena for solutions of some nonlinear evolution equations (Sections 10 to 13).