Related papers: A general asymptotic decay lemma for elliptic prob…

We prove optimal decay estimates for positive solutions to elliptic p-Laplacian problems in the entire Euclidean space, when a critical nonlinearity with a decaying source term is considered. Also gradient decay estimates are furnished. Our…

We prove local decay estimates for the wave equation in the asymptotically Euclidean setting. In even dimensions we go beyond the optimal decay by providing the large time asymptotic profile, given by a solution of the free wave equation.…

We consider a nonlinear parabolic equation with an exponential nonlinearity which is critical with respect to the growth of the nonlinearity and the regularity of the initial data. After showing the equivalence of the notions of weak and…

We study the long-time dynamics of the Navier-Stokes equations in the three-dimensional periodic domains with a body force decaying in time. We introduce appropriate systems of decaying functions and corresponding asymptotic expansions in…

We consider a renewal-like recursion and prove that the solution is polynomially decaying asymptotically under suitable conditions. We prove similar results for the corresponding integral equation. In both cases coefficients and functions…

We derive sufficient conditions for asymptotic and monotone exponential decay in mean square of solutions of the geometric Brownian motion with delay. The conditions are written in terms of the parameters and are explicit for the case of…

We prove a general perturbation theorem that can be used to obtain pairs of nontrivial solutions of a wide range of local and nonlocal nonhomogeneous elliptic problems. Applications to critical $p$-Laplacian problems, $p$-Laplacian problems…

We establish new asymptotic results for the solutions of the second-grade fluids equations and characterize their decay rate in terms of the behavior of the initial data. Moreover, assuming more regularity for the initial data, we study the…

Asymptotic formula is derived for the behavior of the fundamental solution of the second-order elliptic self-adjoint operator with a piecewise-smooth coefficient in front of the senior derivatives near the discontinuity surface of the…

The paper is devoted to the study of asymptotic behavior of solutions for nonlocal elliptic problems in weighted spaces. We deal with the most difficult case where the support of nonlocal terms intersects with the boundary of a plane…

In this paper, we study some anisotropic singular perturbations for a class of linear elliptic problems. We show a global asymptotic expansion of the solution in certain functional space.

In this paper we focus on the initial value problem for quasi-linear dissipative plate equation in multi-dimensional space $(n\geq2)$. This equation verifies the decay property of the regularity-loss type, which causes the difficulty in…

In a decision-theoretic framework, the minimax lower bound provides the worst-case performance of estimators relative to a given class of statistical models. For parametric and semiparametric models, the H\'{a}jek--Le Cam local asymptotic…

In this paper we study a semilinear elliptic problem on a bounded domain in $\R^2$ with large exponent in the nonlinear term. We consider positive solutions obtained by minimizing suitable functionals. We prove some asymtotic estimates…

We consider weak solutions of the adjoint equation for an elliptic operator in nondivergent form, and their asymptotic properties at an interior point. We assume that the coefficients a_{ij} are bounded, measurable, complex-valued functions…

This paper is concerned with investigating the asymptotic behavior of the gradients of solutions to a class of elliptic systems with general boundary data, especially covering the Lam\'{e} systems, in a narrow region. The novelty of this…

We use "generalized" version of total variation, coarea formulas, isoperimetric inequalities to obtain sharp estimates for solutions (and for their gradients) to anisotropic elliptic equations with a lower order term, comparing them with…

This paper studies, in fine details, the long-time asymptotic behavior of decaying solutions of a general class of dissipative systems of nonlinear differential equations in complex Euclidean spaces. The forcing functions decay, as time…

In this paper we study elliptic equations with a nonlinear conormal derivative boundary condition involving nonstandard growth terms. By means of the localization method and De Giorgi's iteration technique we derive global a priori bounds…

We consider a class of quasi-linear anisotropic elliptic equations, possibly degenerate or singular, which are of interest in several applications such as computer vision and continuum mechanics. We prove a Hopf Lemma as well as local and…