On a nonlinear wave equation in unbounded domains.
Our aim in this paper is to study the existence of solutions to a phase-field system based on the Maxwell-Cattaneo heat conduction law, with a logarithmic nonlinearity. In particular, we prove, in one and two space dimensions, the existence of a solution which is separated from the singularities of the nonlinear term.
We prove existence/nonexistence and uniqueness of positive entire solutions for some semilinear elliptic equations on the Hyperbolic space.
We prove an existence theorem of Cauchy-Kovalevskaya type for the equation where f is a polynomial with respect to the last k variables.
We obtain new variants of weighted Gagliardo-Nirenberg interpolation inequalities in Orlicz spaces, as a consequence of weighted Hardy-type inequalities. The weights we consider need not be doubling.
We consider the problem of minimizing the energyamong all functions for which two level sets have prescribed Lebesgue measure . Subject to this volume constraint the existence of minimizers for is proved and the asymptotic behaviour of the solutions is investigated.
We consider the problem of minimizing the energy among all functions u ∈ SBV²(Ω) for which two level sets have prescribed Lebesgue measure . Subject to this volume constraint the existence of minimizers for E(.) is proved and the asymptotic behaviour of the solutions is investigated.
We consider a random, uniformly elliptic coefficient field on the lattice . The distribution of the coefficient field is assumed to be stationary. Delmotte and Deuschel showed that the gradient and second mixed derivative of the parabolic Green’s function satisfy optimal annealed estimates which are and , respectively, in probability, i.e., they obtained bounds on and . In particular, the elliptic Green’s function satisfies optimal annealed bounds. In their recent work, the authors...