Sobolev Exponent Research Articles

Design of regular nonseparable bidimensional wavelets using Grobner basis techniques

The design of two-dimensional (2-D) filter banks yielding orthogonality and linear-phase filters and generating regular wavelet bases is a difficult task involving the algebraic properties of multivariate polynomials. Using cascade forms implies dealing with nonlinear optimization. We turn the issue of optimizing the orthogonal linear-phase cascade from Kovacevic and Vetterli (1992) into a polynomial problem and solve it using Grobner basis techniques and computer algebra. This leads to a complete description of maximally flat wavelets among the orthogonal linear-phase family proposed by Kovacevic and Vetterli. We obtain up to five degrees of flatness for a 16/spl times/16 filter bank, whose Sobolev exponent is 2.11, making this wavelet the most regular orthogonal linear-phase nonseparable wavelet to the authors' knowledge,.

Solubility of non-linear elliptic systems in spaces that are weaker than the natural energy space

We introduce a scale of spaces that are dual to the classical Morrey space. We establish the solubility of non-linear elliptic systems on an interval of this scale, the range of the interval being essentially dependent on the modulus of ellipticity of the system. As a consequence, we prove solubility when the right-hand side is (1) a Lebesgue space with exponent weaker than the Sobolev exponent, (2) a space of densities of finite Borel measure, and (3) a Hardy space for p≤1 under certain restrictions on the modulus of ellipticity. We prove the existence and good behaviour of solutions of fundamental type. Our results are also completely new for linear systems with bounded discontinuous coefficients.

Local behavior of singular positive solutions of semilinear elliptic equations with Sobolev exponent

Local behavior of singular positive solutions of semilinear elliptic equations with Sobolev exponent

Morse index versus concentration for elliptic problems with sobolev exponent

Morse index versus concentration for elliptic problems with sobolev exponent