A semi-linear elliptic equation in a strip arising in a two-dimensional flame propagation model.
A semilinear elliptic problem involving nonlinear boundary condition and sign-changing potential.
A semilinear equation in
A semilinear perturbation of the identity in Hilbert spaces.
A sequential iteration algorithm with non-monotoneous behaviour in the method of projections onto convex sets
The method of projections onto convex sets to find a point in the intersection of a finite number of closed convex sets in a Euclidean space, may lead to slow convergence of the constructed sequence when that sequence enters some narrow “corridor” between two or more convex sets. A way to leave such corridor consists in taking a big step at different moments during the iteration, because in that way the monotoneous behaviour that is responsible for the slow convergence may be interrupted. In this...
A set of axioms for the degree of a tangent vector field on differentiable manifolds.
A sharp rearrangement inequality for the fractional maximal operator
We prove a sharp pointwise estimate of the nonincreasing rearrangement of the fractional maximal function of ⨍, , by an expression involving the nonincreasing rearrangement of ⨍. This estimate is used to obtain necessary and sufficient conditions for the boundedness of between classical Lorentz spaces.
A sharp result on the exponential operator-norm decay of a family of strongly continuous semigroups.
A Short Proof of Radjavi's Theorem on Self-Commutators.
A Short Proof of the Ando-Krieger Theorem.
A short proof of the best possibility for the grand Furuta inequality.
A shrinking projection method for generalized mixed equilibrium problems, variational inclusion problems and a finite family of quasi-nonexpansive mappings.
A simple characterization of the trace-class of operators.
A Simple Example of Localized Parametric Resonance for the Wave Equation
2000 Mathematics Subject Classification: 35L05, 35P25, 47A40.The problem studied here was suggested to us by V. Petkov. Since the beginning of our careers, we have benefitted from his insights in partial differential equations and mathematical physics. In his writings and many discussions, the conjuction of deep analysis and specially interesting problems has been a source inspiration for us.The research of J. Rauch is partially supported by the U.S. National Science Foundation under grant NSF-DMS-0104096...
A simple proof of polar decomposition in pseudo-Euclidean geometry
We give a simple direct proof of the polar decomposition for separated linear maps in pseudo-Euclidean geometry.
A simple proof of the Borel extension theorem and weak compactness of operators
Let be a locally compact Hausdorff space and let be the Banach space of all complex valued continuous functions vanishing at infinity in , provided with the supremum norm. Let be a quasicomplete locally convex Hausdorff space. A simple proof of the theorem on regular Borel extension of -valued -additive Baire measures on is given, which is more natural and direct than the existing ones. Using this result the integral representation and weak compactness of a continuous linear map when...
A simple proof of the classification of normal Toeplitz matrices.
A simple proof of the continuity of the higher order Riesz transforms with respect to the gaussian measure
A simple proof of the Poincaré inequality for a large class of probability measures.
A simple regularization method for the ill-posed evolution equation
The nonhomogeneous backward Cauchy problem , where is a positive self-adjoint unbounded operator which has continuous spectrum and is a given function being given is regularized by the well-posed problem. New error estimates of the regularized solution are obtained. This work extends earlier results by N. Boussetila and by M. Denche and S. Djezzar.