Scaling limits and regularity results for a class of Ginzburg-Landau systems
Schauder theorems for linear elliptic and parabolic problems with unbounded coefficients in
We study existence, uniqueness, and smoothing properties of the solutions to a class of linear second order elliptic and parabolic differential equations with unbounded coefficients in . The main results are global Schauder estimates, which hold in spite of the unboundedness of the coefficients.
Second order parabolic systems, optimal regularity, and singular sets of solutions
Semielliptic singularities
Semilinear parabolic systems
Semilinear wave equations with angularly smooth data
Semilinear waves with cusp singularities
Serrin-type regularity criterion for the Navier-Stokes equations involving one velocity and one vorticity component
We consider the Cauchy problem for the three-dimensional Navier-Stokes equations, and provide an optimal regularity criterion in terms of and , which are the third components of the velocity and vorticity, respectively. This gives an affirmative answer to an open problem in the paper by P. Penel, M. Pokorný (2004).
Sharp asymptotic estimates for vorticity solutions of the 2D Navier-Stokes equation.
Sharp regularity theory for second order hyperbolic equations of Neumann type
This note provides sharp regularity results for general, time-independent, second order, hyperbolic equations with non-homogeneous data of Neumann type.
Shigesada-Kawasaki-Teramoto model on higher dimensional domains.
Singular nonlinear elliptic equations in .
Singular solutions of elliptic boundary value problems in polyhedra
Singular Solutions of the p-Laplace Equation.
Singular Solutions of the p-Laplace Equation (Erratum).
Singular solutions to linear elliptic systems
Singularities of eddy current problems
We consider the time-harmonic eddy current problem in its electric formulation where the conductor is a polyhedral domain. By proving the convergence in energy, we justify in what sense this problem is the limit of a family of Maxwell transmission problems: Rather than a low frequency limit, this limit has to be understood in the sense of Bossavit [11]. We describe the singularities of the solutions. They are related to edge and corner singularities of certain problems for the scalar Laplace operator,...
Singularities of eddy current problems
We consider the time-harmonic eddy current problem in its electric formulation where the conductor is a polyhedral domain. By proving the convergence in energy, we justify in what sense this problem is the limit of a family of Maxwell transmission problems: Rather than a low frequency limit, this limit has to be understood in the sense of Bossavit [11]. We describe the singularities of the solutions. They are related to edge and corner singularities of certain problems for the scalar Laplace...
Smooth regularity for solutions of the Levi Monge-Ampère equation
We present a smooth regularity result for strictly Levi convex solutions to the Levi Monge-Ampère equation. It is a fully nonlinear PDE which is degenerate elliptic. Hence elliptic techniques fail in this situation and we build a new theory in order to treat this new topic. Our technique is inspired to those introduced in [3] and [8] for the study of degenerate elliptic quasilinear PDE’s related to the Levi mean curvature equation. When the right hand side has the meaning of total curvature of a...
Smooth solutions of systems of quasilinear parabolic equations
We consider in this article diagonal parabolic systems arising in the context of stochastic differential games. We address the issue of finding smooth solutions of the system. Such a regularity result is extremely important to derive an optimal feedback proving the existence of a Nash point of a certain class of stochastic differential games. Unlike in the case of scalar equation, smoothness of solutions is not achieved in general. A special structure of the nonlinear hamiltonian seems to be the...