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In this paper, we propose a variational formulation to study the singular evolution equations that govern the dynamics of surface modulations on crystals below the roughening temperature. The basic idea of the formulation is to expand the…

We establish the higher differentiability of solutions to a class of obstacle problems for integral functionals where the convex integrand f satisfies p-growth conditions with respect to the gradient variable. We derive that the higher…

We study monotone numerical schemes for nonlocal Isaacs equations, the dynamic programming equations of stochastic differential games with jump-diffusion state processes. These equations are fully-nonlinear non-convex equations of order…

In this paper, we study diagonalizable hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and nondecreasing initial data. Moreover, we show…

Two different types of generalized solutions, namely viscosity and variational solutions, were introduced to solve the first-order evolutionary Hamilton--Jacobi equation. They coincide if the Hamiltonian is convex in the momentum variable.…

We establish a local minimality sufficiency criterion, based on the strict positivity of the second variation, in the context of a variational model for the epitaxial growth of elastic films. Our result holds also in the three-dimensional…

In this paper, we study a second-order, nonlinear evolution equation with damping arising in elastodynamics. The nonlinear term is monotone and possesses a convex potential but exhibits anisotropic and nonpolynomial growth. The appropriate…

We consider a possibly anisotropic integro-differential semilinear equation, run by a nondecreasing and nontrivial nonlinearity. We prove that if the solution grows at infinity less than the order of the operator, then it must be constant.

The nonlinear hyperbolic system of pde's governing the evolution of the deformation of isotropic hyperelastic materials is considered. In the absence of boundaries and with an additional nonresonance or null condition, the system has global…

In this paper we investigate continuity properties of first and second order shape derivatives of functionals depending on second order elliptic PDE's around nonsmooth domains, essentially either Lipschitz or convex, or satisfying a uniform…

Constraints on changes in expression levels across all cell components imposed by the steady growth of cells have recently been discussed both experimentally and theoretically. By assuming a small environmental perturbation and considering…

We investigate local and global strong solutions for the incompressible viscoelastic system of Oldroyd--B type. We obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated…

For nonautonomous linear difference equations in Banach spaces we show that a very general type of dichotomic behavior persists under small enough additive linear perturbations. By using a new approach, we obtain two general robustness…

With the terminal value $|\xi|$ admitting some given exponential moment, we put forward and prove several existence and uniqueness results for the unbounded solutions of quadratic backward stochastic differential equations whose generators…

We construct viscosity solutions to the nonlinear evolution equation \eqref{p} below which generalizes the motion of level sets by mean curvature (the latter corresponds to the case $p = 1$) using the regularization scheme as in \cite{ES1}…

We study the large time behavior of solutions of first-order convex Hamilton-Jacobi Equations of Eikonal type set in the whole space. We assume that the solutions may have arbitrary growth. A complete study of the structure of solutions of…

This paper considers the growth rates of positive solutions of scalar nonlinear functional and Volterra differential equations. The equations are assumed to be autonomous (or asymptotically so), and the nonlinear dependence grows less…

We are concerned with the study of the well-posedness of a nonlinear diffusion equation with a monotonically increasing multivalued time-dependent nonlinearity derived from a convex continuous potential having a superlinear growth to…

In this paper we obtain regularity results for elliptic integro-differential equations driven by the stronger effect of coercive gradient terms. This feature allows us to construct suitable strict supersolutions from which we conclude…

We investigate memory dependent asymptotic growth in scalar Volterra equations with sublinear nonlinearity. To obtain precise results we utilise the powerful theory of regular variation extensively. By computing the growth rate in terms of…