Everywhere regularity for a class of vectorial functionals under subquadratic general growth conditions

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Local boundedness for solutions of a class of nonlinear elliptic systems

In this paper we are concerned with the regularity of solutions to a nonlinear elliptic system of m equations in divergence form, satisfying p growth from below and q growth from above, with p <= q; this case is known as p, q-growth conditions. Well known counterexamples, even in the simpler case p = q, show that solutions to systems may be singular; so, it is necessary to add suitable structure conditions on the system that force solutions to be regular. Here we obtain local boundedness of solutions under a componentwise coercivity condition. Our result is obtained by proving that each component u(alpha) of the solution u = (u(1),..., u(m)) satisfies an improved Caccioppoli's inequality and we get the boundedness of u(alpha) by applying De Giorgi's iteration method, provided the two exponents p and q are not too far apart. Let us remark that, in dimension n = 3 and when p = q, our result works for 3/2 < p <= 3, thus it complements the one of Bjorn whose technique allowed her to deal with p <= 2 only. In the final section, we provide applications of our result

On the H\uf6lder continuity for a class of vectorial problems

In this paper we prove local H\uf6lder continuity of vectorial local minimizers of special classes of integral functionals with rank-one and polyconvex integrands. The energy densities satisfy suitable structure assumptions and may have neither radial nor quasi-diagonal structure. The regularity of minimizers is obtained by proving that each component stays in a suitable De Giorgi class and, from this, we conclude about the H\uf6lder continuity. In the final section, we provide some non-trivial applications of our results

Artificial neural networks for 3D cell shape recognition from confocal images

We present a dual-stage neural network architecture for analyzing fine shape details from microscopy recordings in 3D. The system, tested on red blood cells, uses training data from both healthy donors and patients with a congenital blood disease. Characteristic shape features are revealed from the spherical harmonics spectrum of each cell and are automatically processed to create a reproducible and unbiased shape recognition and classification for diagnostic and theragnostic use.Comment: 17 pages, 8 figure

What is the right theory for Anderson localization of light?

Anderson localization of light is traditionally described in analogy to electrons in a random potential. Within this description the disorder strength -- and hence the localization characteristics -- depends strongly on the wavelength of the incident light. In an alternative description in analogy to sound waves in a material with spatially fluctuating elastic moduli this is not the case. Here, we report on an experimentum crucis in order to investigate the validity of the two conflicting theories using transverse-localized optical devices. We do not find any dependence of the observed localization radii on the light wavelength. We conclude that the modulus-type description is the correct one and not the potential-type one. We corroborate this by showing that in the derivation of the traditional, potential-type theory a term in the wave equation has been tacititly neglected. In our new modulus-type theory the wave equation is exact. We check the consistency of the new theory with our data using a field-theoretical approach (nonlinear sigma model)