Related papers: Uniform H\"older regularity with small exponent in…
We investigate existence and regularity of weak solutions of a 1-dimensional parabolic differential equation with a non-constant H\"older diffusion coefficient and a rough forcing term. Such an equation appears in studying the 1-dimensional…
In this article we study optimization problems ruled by $\alpha$-fractional diffusion operators with volume constraints. By means of penalization techniques we prove existence of solutions. We also show that every solution is locally of…
The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential…
We investigate systems of nature where the common physical processes diffusion and fragmentation compete. We derive a rate equation for the size distribution of fragments. The equation leads to a third order differential equation which we…
We study a quasilinear chemotaxis system of singular type, where the diffusion operator is given by $\Delta u^m$ with $0<m<1$, corresponding to the fast diffusion regime, and where the chemotactic drift is nonlinear. Since H\"older…
We study a quite general family of nonlinear evolution equations of diffusive type with nonlocal effects. More precisely, we study porous medium equations with a fractional Laplacian pressure, and the problem is posed on a bounded space…
We establish the boundedness of solutions of reaction-diffusion systems with quadratic (in fact slightly super-quadratic) reaction terms that satisfy a natural entropy dissipation property, in any space dimension N>2. This bound imply the…
We investigate a class of three-component reaction-diffusion systems subject to mass control and a newly introduced structural assumption, referred to as linear intermediate weighted sum condition. Under these hypotheses, we establish the…
Homogenization of a stochastic nonlinear reaction-diffusion equation with a large non- linear term is considered. Under a general Besicovitch almost periodicity assumption on the coefficients of the equation we prove that the sequence of…
We study a diffusive Lotka-Volterra competition system with advection under Neumann boundary conditions. Our system models a competition relationship that one species escape from the region of high population density of their competitors in…
Given a hyperbolic homeomorphism on a compact metric space, consider the space of linear cocycles over this base dynamics which are H\"older continuous and whose projective actions are partially hyperbolic dynamical systems. We prove that…
We study well-posedness and equivalence of different notions of solutions with finite energy for nonlocal porous medium type equations of the form $$\partial_tu-A\varphi(u)=0.$$ These equations are possibly degenerate nonlinear diffusion…
The main objective of this paper is analysis of the initial-boundary value problems for the linear and semilinear time-fractional diffusion equations with a uniformly elliptic spatial differential operator of the second order and the Caputo…
We provide several regularity results for non-homogeneous drift-diffusion equations with applications to general dissipative SQG. Our results unify in a rather simple way several previously known results. We build the estimates on an…
We provide explicit classical solutions and stochastic analogues for distributed-order space-time fractional diffusion equations on bounded domains with zero exterior boundary conditions. We also show that our results still hold when the…
We study thin obstacle problems involving the energy functional with $p(x)$-growth. We prove higher integrability and H\"{o}lder regularity for the gradient of minimizers of the thin obstacle problems under the assumption that the variable…
In this article we show a $C^{0,\alpha}$-partial regularity result for solutions of a certain class of cross-diffusion systems with entropy structure. Under slightly more stringent conditions on the system, we are able to obtain a…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
A mean-field-type limit from stochastic moderately interacting many-particle systems with singular Riesz potential is performed, leading to nonlocal porous-medium equations in the whole space. The nonlocality is given by the inverse of a…
We consider equations involving a combination of local and nonlocal degenerate $p$-Laplace operators. The main contribution of the paper is almost Lipschitz regularity for the homogeneous equation and H\"older continuity with an explicit…