We consider linear boundary value problems for higher-order parameter-elliptic equations, where the data do not belong to classical trace spaces. employ a class of Sobolev spaces mixed smoothness that admits generalized with values in Besov negative order. prove unique solvability rough half-space and sufficiently smooth domains. As an application, we show operator related linearized Cahn–Hilli...

In this work, we demonstrate the Wong-Zakai approximation results for two- and three-dimensional stochastic convective Brinkman-Forchheimer (SCBF) equations forced by Hilbert space valued Wiener noise on bounded domains. Even though existence uniqueness of a pathwise strong solution to SCBF is known, unique approximating system not immediate from solvability equations, prove it using Faedo-Gale...

In this paper, we consider dynamical models and we study the preservation of solvability for the Disturbance Rejection by Measurement Feedback (DRMF) problem under sensor failure in a structural framework. We consider a linear structured system and we wonder if the DRMF problem remains solvable in case of some sensor failure. More precisely we will characterize among the sensors some of those w...

We establish a connection between the absolute continuity of elliptic measure associated to a second order divergence form operator with bounded measurable coefficients with the solvability of an endpoint BMO Dirichlet problem. We show that these two notions are equivalent. As a consequence we obtain an end-point perturbation result, i.e., the solvability of the BMO Dirichlet problem implies Lp...

This paper studies the dominance-solvability (by iterated deletion of weakly dominated strategies) of general scoring rule voting games. The scoring rules we study include Plurality rule, Approval voting, Negative Plurality Rule, Borda rule and Relative Utilitarianism. We provide a classification of scoring rule voting games according to whether the sufficient conditions for dominance solvabili...

This article is concerned with the study of unique solvability a timenonlocal inverse boundary value problem for second-order hyperbolic equation an integral overdetermination condition. To problem, we first reduce considered to auxiliary system trivial data and prove its equivalence (in certain sense) original problem. Then using Banach fixed point principle, existence uniqueness solution this...

We prove the unique solvability, passivity/conservativity and some regularity results of two mathematical models for acoustic wave propagation in curved, variable diameter tubular structures of finite length. The first of the models is the generalised Webster’s model that includes dissipation and curvature of the 1D waveguide. The second model is the scattering passive, boundary controlled wave...

Abatraet-We study the selection of the shape and growth velocity of three dimensionaf dendritic crystals in cubically anisotropic materials. We demonstrate that aside from minor additional complexities due to the lack of axisymmetry, the recently discovered mechanism of “microscopic solvability” can be extended to these systems and used to find a unique needle crystal solution of the equations ...

Martin COSTABEL & Monique DAUGE Abstract. The 2 2 system of integral equations corresponding to the biharmonic single layer potential in R2 is known to be strongly elliptic. It is also known to be positive definite on a space of functions orthogonal to polynomials of degree one. We study the question of its unique solvability without this orthogonality condition. To each curve , we associate a ...