Radial solutions for a nonlocal boundary value problem.
Radial solutions to a superlinear Dirichlet problem using Bessel functions.
Radiation conditions at the top of a rotational cusp in the theory of water-waves
We study the linearized water-wave problem in a bounded domain (e.g.a finite pond of water) of , having a cuspidal boundary irregularity created by a submerged body. In earlier publications the authors discovered that in this situation the spectrum of the problem may contain a continuous component in spite of the boundedness of the domain. Here, we proceed to impose and study radiation conditions at a point of the water surface, where a submerged body touches the surface (see Fig. 1). The radiation...
Radiation conditions at the top of a rotational cusp in the theory of water-waves
We study the linearized water-wave problem in a bounded domain (e.g. a finite pond of water) of , having a cuspidal boundary irregularity created by a submerged body. In earlier publications the authors discovered that in this situation the spectrum of the problem may contain a continuous component in spite of the boundedness of the domain. Here, we proceed to impose and study radiation conditions at a point of the water surface, where a submerged body touches the surface (see Fig. 1)....
Reflection principles for Laplace's equation when the boundary data involves derivatives of higher order
Regular eigenvalue problem with eigenparameter contained in the equation and the boundary conditions.
Regular oblique derivative problem in Morrey spaces.
Regular regions for parabolic and elliptic equations
Régularité de la solution d'un problème aux limites unilatéral dans un domaine convexe
Régularité höldérienne de certains problèmes aux limites elliptiques dégénérés
Régularité höldérienne de certains problèmes aux limites elliptiques singuliers
Régularité höldérienne de certains problèmes aux limites elliptiques dégénérés
Regularity at infinity for a mixed problem for degenerate elliptic operators in a half-cylinder.
Regularity in free boundary problems
Regularity in Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients.
Regularity of domains of parameterized families of closed linear operators
The purpose of this paper is to provide a method of reduction of some problems concerning families of linear operators with domains to a problem in which all the operators have the same domain . To do it we propose to construct a family of automorphisms of a given Banach space X having two properties: (i) the mapping is sufficiently regular and (ii) for t ∈ . Three effective constructions are presented: for elliptic operators of second order with the Robin boundary condition with a parameter;...
Regularity of renormalized solutions to nonlinear elliptic equations away from the support of measure data
We prove boundedness and continuity for solutions to the Dirichlet problem for the equation where the left-hand side is a Leray-Lions operator from into with , is a Carathéodory function which grows like and is a finite Radon measure. We prove that renormalized solutions, though not globally bounded, are Hölder-continuous far from the support of .
Regularity of the optimal shape for the first eigenvalue of the laplacian with volume and inclusion constraints
Regularity of the Poisson kernel and free boundary problems
Regularity of the solution of some transmission problems in domains with cuspidal point
Regularity results for transmission problems in domains with (outgoing) cuspidal points are considered. We prove in some special but generic situations that the solution is piecewise in .