The Stefan problem in heterogeneous media
The Stefan problem with kinetic condition at the free boundary
The Stokes system in the incompressible case-revisited
The classical Stokes system is reconsidered and reformulated in a functional analytical setting allowing for low regularity of the data and the boundary. In fact the underlying domain can be any non-empty open subset Ω of ℝ³. A suitable solution concept and a corresponding solution theory is developed.
The successive approximation method for the Dirichlet problem in a planar domain
The Dirichlet problem for the Laplace equation for a planar domain with piecewise-smooth boundary is studied using the indirect integral equation method. The domain is bounded or unbounded. It is not supposed that the boundary is connected. The boundary conditions are continuous or p-integrable functions. It is proved that a solution of the corresponding integral equation can be obtained using the successive approximation method.
The summability of solutions to variational problems since Guido Stampacchia.
Inequalities concerning the integral of |∇u|2 on the subsets where |u(x)| is greater than k can be used in order to prove regularity properties of the function u. This method was introduced by Ennio De Giorgi e Guido Stampacchia for the study of the regularity of the solutions of Dirichlet problems.
The support shrinking properties for solutions of quasilinear parabolic equations with strong absorption terms
The surjectivity of a constant coefficient homogeneous differential operator in the real analytic functions and the geometry of its symbol
Hörmander has characterized the surjective constant coefficient partial differential operators on the space of all real analytic functions on by a Phragmén-Lindelöf condition. Geometric implications of this condition and, for homogeneous operators, of the corresponding condition for Gevrey classes are given.
The symbol of a lagrangian distribution
The symmetry algebra and conserved Currents for Klein-Gordon equation on quantum Minkowski space
The symmetry operators for Klein-Gordon equation on quantum Minkowski space are derived and their algebra is studied. The explicit form of the Leibniz rules for derivatives and variables for the case Z=0 is given. It is applied then with symmetry operators to the construction of the conservation law and the explicit form of conserved currents for Klein-Gordon equation.
The symmetry of minimizing harmonic maps from a two dimensional domain to the sphere
The Tartar equation for homogenization of a model of the dynamics of fine-dispersion mixtures.
The temperature of an asteroid
The theory of small changesin the domain of existence in the theory of partial differential equations and its applications
The thermistor obstacle problem with periodic data
The third boundary value problem for a nonlinear system of second order hyperbolic integro-differential equations
The third boundary value problem in potential theory for domains with a piecewise smooth boundary
The paper investigates the third boundary value problem for the Laplace equation by the means of the potential theory. The solution is sought in the form of the Newtonian potential (1), (2), where is the unknown signed measure on the boundary. The boundary condition (4) is weakly characterized by a signed measure . Denote by the corresponding operator on the space of signed measures on the boundary of the investigated domain . If there is such that the essential spectral radius of is...
The third order spectrum of the p-biharmonic operator with weight
We show that the spectrum of , where , under Navier boundary conditions, contains at least one sequence of eigensurfaces.
The topological asymptotic for the Navier-Stokes equations
The aim of the topological asymptotic analysis is to provide an asymptotic expansion of a shape functional with respect to the size of a small inclusion inserted inside the domain. The main field of application is shape optimization. This paper addresses the case of the steady-state Navier-Stokes equations for an incompressible fluid and a no-slip condition prescribed on the boundary of an arbitrary shaped obstacle. The two and three dimensional cases are treated for several examples of cost functional...
The topological asymptotic for the Navier-Stokes equations
The aim of the topological asymptotic analysis is to provide an asymptotic expansion of a shape functional with respect to the size of a small inclusion inserted inside the domain. The main field of application is shape optimization. This paper addresses the case of the steady-state Navier-Stokes equations for an incompressible fluid and a no-slip condition prescribed on the boundary of an arbitrary shaped obstacle. The two and three dimensional cases are treated for several examples of cost functional...
The topological derivative of the Dirichlet integral under formation of a thin ligament.