On the optimality of velocity averaging lemmas
On the parameter dependence of solutions to the ...-equation.
On the Partial Regularity of Weak Solutions of Nonlinear Parabolic Systems.
On the precise asymptotics of the constant in Friedrich's inequality for functions vanishing on the part of the boundary with microinhomogeneous structure.
On the rate of the volume growth for symmetric viscous heat-conducting gas flows with a free boundary.
On the regularity of averages over spheres for kinetic transport equations in hyperbolic Sobolev spaces.
On the rigidity of minimal mass solutions to the focusing mass-critical NLS for rough initial data.
On the Schauder estimates of solutions to parabolic equations
On the Schrödinger equation in L...spaces.
On the second order derivatives of convex functions on the Heisenberg group
In the euclidean setting the celebrated Aleksandrov-Busemann-Feller theorem states that convex functions are a.e. twice differentiable. In this paper we prove that a similar result holds in the Heisenberg group, by showing that every continuous –convex function belongs to the class of functions whose second order horizontal distributional derivatives are Radon measures. Together with a recent result by Ambrosio and Magnani, this proves the existence a.e. of second order horizontal derivatives for...
On the solvability of a nonlocal problem arising in dynamics of moisture transfer.
On the solvability of nonlocal pluriparabolic problems.
On the solvability of parabolic and hyperbolic problems with a boundary integral condition.
On the stability of the Dirichlet problem for the vibrating string equation
On the Stefan problem with a small parameter
We consider the multidimensional two-phase Stefan problem with a small parameter κ in the Stefan condition, due to which the problem becomes singularly perturbed. We prove unique solvability and a coercive uniform (with respect to κ) estimate of the solution of the Stefan problem for t ≤ T₀, T₀ independent of κ, and the existence and estimate of the solution of the Florin problem (Stefan problem with κ = 0) in Hölder spaces.
On the structure of solutions to elliptic problems with strong anisotropy.
On the uniform boundedness of the solutions of systems of reaction-diffusion equations.
On the uniqueness of the second bound state solution of a semilinear equation
On the validity of Friedrichs' inequalities.
On the viscous Allen-Cahn and Cahn-Hilliard systems with Willmore regularization
We consider the viscous Allen-Cahn and Cahn-Hilliard models with an additional term called the nonlinear Willmore regularization. First, we are interested in the well-posedness of these two models. Furthermore, we prove that both models possess a global attractor. In addition, as far as the viscous Allen-Cahn equation is concerned, we construct a robust family of exponential attractors, i.e. attractors which are continuous with respect to the perturbation parameter. Finally, we give some numerical...