Related papers: Optimal boundary regularity for fast diffusion equ…
The aim of this note is to present preliminary existence results for a system of cross-diffusion equations defined on a domain with moving boundaries, which model the evolution of the concentrations of different chemical species in a solid…
We classify regularity for Lagrangian mean curvature type equations, which include the potential equation for prescribed Lagrangian mean curvature and those for Lagrangian mean curvature flow self-shrinkers and expanders, translating…
We consider the Cauchy problem for two prototypes of flux-saturated diffusion equations. In arbitrary space dimension, we give an optimal condition on the growth of the initial datum which discriminates between occurrence or nonoccurrence…
In this note we propose the exact artificial boundary conditions formula to the fractional reaction-subdiffusion equation on an unbounded domain. With the application of Laplace transformation, the exact artificial boundary conditions…
We obtain a priori estimates with best constants for the solutions of the fractional fast diffusion equation $u_t+(-\Delta)^{\sigma/2}u^m=0$, posed in the whole space with $0<\sigma<2$, $0<m\le 1$. The estimates are expressed in terms of…
Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter, are considered. Using an interior Dirichlet heat kernel lower bound estimate for…
This work develops moment bounds for the controlled rough path norm of the solution of semilinear rough partial differential equations.~The novel aspects are two-fold: first we consider rough paths of low time regularity…
We consider systems of reaction-diffusion equations coupled in zero order terms, with general homogeneous boundary conditions in domains with a particular geometry (annular type domains). We establish Lipschitz stability estimates in L^2…
The use of fully or partially absorbing boundary conditions for diffusion-based problems has become paradigmatic in physical chemistry and biochemistry to describe reactions occurring in solutions or in living media. However, as chemical…
A system of Boundary-Domain Integral Equations is derived from the mixed (Dirichlet-Neumann) boundary value problem for the diffusion equation in inhomogeneous media defined on an unbounded domain. Boundary-domain integral equations are…
We show that finite-energy weak solutions to the incompressible Navier--Stokes equations on a three-dimensional bounded smooth domain are regular up to the boundary, provided that the $L^4_tL^4_x$-norm of the solution is smaller than a…
We investigate a coagulation-fragmentation equation with boundary data, establishing the well-posedness of the initial value problem when the coagulation kernels are bounded at zero and showing existence of solutions for the singular…
We provide regularity results at the boundary for continuous viscosity solutions to nonconvex fully nonlinear uniformly elliptic equations and inequalities in Euclidian domains. We show that (i) any solution of two sided inequalities with…
We study a higher order analogue to the Alt-Caffarelli functional that arises in several shape optimization problems, among which the minimization of the critical buckling load of a clamped plate of fixed area. We obtain several regularity…
We prove some sharp regularity results for solutions of classical first order hyperbolic initial boundary value problems. Our two main improvements on the existing litterature are weaker regularity assumptions for the boundary data and…
We establish H\"older regularity for the weak solution to a degenerate diffusion equation in the presence of a local (drift) potential and nonlocal (interaction) term, posed in a bounded domain with no-flux boundary conditions. The…
In this paper, we investigate the solvability, regularity and the vanishing dissipation limit of solutions to the three-dimensional viscous magneto-hydrodynamic (MHD) equations in bounded domains. On the boundary, the velocity field…
We consider the finite element discretization and the iterative solution of singularly perturbed elliptic reaction-diffusion equations in three-dimensional computational domains. These equations arise from the optimality conditions for…
We establish rigorous quantitative inequalities for the first eigenvalue of the generalized $p$-Robin problem, for both the classical diffusion absorption case, where the Robin boundary parameter $\alpha$ is positive, and the…
We prove the partial regularity of the boundary suitable weak solutions to the MHD system near the plane part of the boundary.