Related papers: A symmetry result for polyharmonic problems with N…
We study the existence of nontrivial weak solutions for a class of generalized $p(x)$-biharmonic equations with singular nonlinearity and Navier boundary condition. The proofs combine variational and topological arguments. The approach…
We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction,…
In this paper we prove symmetry results for classical solutions of nonlinear cooperative elliptic systems in a ball or in annulus in R^N, with N greather or equal than 2. More precisely we prove that solutions having Morse index j smaller…
This paper is concerned with the analysis of elastic wave scattering of a time-harmonic plane wave by a biperiodic rigid surface, where the wave propagation is governed by the three-dimensional Navier equation. An exact transparent boundary…
We show that in $\mathbb{C}^2$ if the set of strongly regular points are closed in the boundary of a smooth bounded pseudoconvex domain, then the domain is c-regular, that is, the plurisubharmonic upper envelopes of functions continuous up…
By virtue of a weak comparison principle in small domains we prove axial symmetry in convex and symmetric smooth bounded domains as well as radial symmetry in balls for regular solutions of a class of quasi-linear elliptic systems in…
In this paper we show the existence of strictly monotone heteroclinic type solutions of semilinear elliptic equations in cylinders. The motivation of this construction is twofold: first, it implies the existence of an entire bounded…
We prove existence of global regular axially-symmetric solutions to the Navier-Stokes equations in a cylindrical domain. We assume the periodic boundary conditions on the top and the bottom of the cylinder, but on the lateral part we assume…
We discuss a time-harmonic inverse scattering problem for the Navier equation with compactly supported penetrable and possibly inhomogeneous scattering objects in an unbounded homogeneous background medium, and we develop a monotonicity…
We prove the one-dimensional symmetry of solutions to elliptic equations of the form $-\dive(e^{G(x)}a(|\nabla u|)\nabla u)=f(u) e^{G(x)}$, under suitable energy conditions. Our results hold without any restriction on the dimension of the…
We consider positive solutions to $\displaystyle -\Delta_p u=\frac{1}{u^\gamma}+f(u)$ under zero Dirichlet condition in the half space. Exploiting a prio-ri estimates and the moving plane technique, we prove that any solution is monotone…
The full ``classical" Dirac-Maxwell equations are considered under various simplifying assumptions. A reduction of the equations is performed in the case when the Dirac field is {\em static} and a further reduction is performed in the case…
A particular mix of integral equations and discretization techniques is suggested for the solution of a planar Helmholtz transmission problem with relevance to the study of surface plasmon waves. The transmission problem describes the…
In this paper we first study the penalization approximation of stochastic differential equations reflected in a domain which satisfies conditions (A) and (B) and prove that the sequence of solutions of the penalizing equations converges in…
This note should clarify how the behavior of certain invariant objects reflects the geometric convexity of balanced domains.
We construct a special plurisubharmonic defining function for a smoothly bounded strictly pseudoconvex domain so that the determinant of the complex Hessian vanishes to high order on the boundary. This construction, coupled with regularity…
Let C be convex, compact, with nonempty interior and h be Legendre with domain C, continuous on C. We prove that h is Bregman if and only if it is strictly convex on C and C is a polytope. This provides insights on sequential convergence of…
We show that the fundamental tone of the bilaplacian with Dirichlet or Navier boundary conditions on radially symmetric domains is always simple in dimension $N\ge3$. In dimension $N=2$ we show that it is simple if the inner radius is big…
Reflected diffusions in convex polyhedral domains arise in a variety of applications, including interacting particle systems, queueing networks, biochemical reaction networks and mathematical finance. Under suitable conditions on the data,…
We construct sense-preserving univalent harmonic mappings which map the unit disk onto a domain which is convex in the horizontal direction, but with varying dilatation. Also, we obtain minimal surfaces associated with such harmonic…