arXiv subjects
Publications and source records attributed to Filomena De Filippis.
We develop a nonlinear potential theoretic framework for Schauder estimates for vector-valued solutions of a broad class of nonautonomous variational problems at nearly linear growth. Our approach naturally embraces the variable exponent as well as the Double and Multi phase setting, yielding new regularity results in basic models and recovering optimal regularity recently established in specific cases.
We establish local boundedness for solutions to fractional porous medium-type equations in the fast diffusion regime, under optimal tail assumptions.
We investigate the validity and the failure of modular density of smooth maps on compact manifolds.
We investigate partial regularity for vector valued local minimizers of double phase functionals, under vectorial obstacle type constraints satisfying appropriate topological properties.
In the present manuscript we give a structure condition that allows for energy approximation in the vectorial case and we provide two examples, enjoying such a condition.
Bounded minimizers of double phase problems at nearly linear growth have locally H\"older continuous gradient within the sharp maximal nonuniformity range $q<1+\alpha$.
Minima of the log-multiphase variational integral $$ w \mapsto \int_{\Omega} \left[|Dw|\log(1+|Dw|) + a(x)|Dw|^q + b(x)|Dw|^s\right] \, {\rm d}x\,, $$ have locally H\"older continuous gradient under sharp quantitative bounds linking the growth powers $(q,s)$ to the H\"older exponents of the modulating coefficients $a(\cdot)$ and $b(\cdot)$ respectively.
We study classes of weights ensuring the absence and presence of the Lavrentiev's phenomenon for double phase functionals upon every choice of exponents. We introduce a new sharp scale for weights for which there is no Lavrentiev's phenomenon up to a counterexample we provide. This scale embraces the sharp range for $α$-Hölder continuous weights. Moreover, it allows excluding the gap for every choice of exponents $q,p>1$.