相关论文: Regularity of solutions to higher-order integrals …

Problems involving rolling without slipping or no sideways skidding, to name a few, introduce velocity-dependent constraints that can be efficiently treated by the method of Lagrange multipliers in the Lagrangian formulation of the…

A variational principle for Lagrangian densities containing derivatives of real order is formulated and the invariance of this principle is studied in two characteristic cases. Necessary and sufficient conditions for an infinitesimal…

We prove necessary optimality conditions of Euler-Lagrange type for generalized problems of the calculus of variations on time scales with a Lagrangian depending not only on the independent variable, an unknown function and its delta…

A second-order regularity theory is developed for solutions to a class of quasilinear elliptic equations in divergence form, including the $p$-Laplace equation, with merely square-integrable right-hand side. Our results amount to the…

We prove an a priori estimate for the second derivatives of local minimizers of integral functionals of calculus of variation with convex integrand with respect to the gradient variable, assuming that the function that measures the…

We prove optimality conditions for generalized quantum variational problems with a Lagrangian depending on the free end-points. Problems of calculus of variations of this type cannot be solved using the classical theory.

This paper presents necessary and sufficient optimality conditions for problems of the fractional calculus of variations with a Lagrangian depending on the free end-points. The fractional derivatives are defined in the sense of Caputo.

In this note, we prove that minimizers of convex functionals with a convexity constraint and a general class of Lagrangians can be approximated by solutions to fourth-order equations of Abreu type. Our result generalizes that of Le (Twisted…

We obtain necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative, a fractional and an indefinite integral. Main results give fractional Euler-Lagrange type equations and…

A partial regularity theorem is presented for minimisers of $k$th-order functionals subject to a quasiconvexity and general growth condition. We will assume a natural growth condition governed by an $N$-function satisfying the $\Delta_2$…

In this article we study convex non-autonomous variational problems with differential forms and corresponding function spaces. We introduce a general framework for constructing counterexamples to the Lavrentiev gap, which we apply to…

An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators. In this…

We prove a necessary optimality condition of Euler--Lagrange type for the calculus of variations with Omega derivatives, which turns out to be sufficient under jointly convexity of the Lagrangian.

We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the…

In this work we look at the original fractional calculus of variations problem in a somewhat different way. As a simple consequence, we show that a fractional generalization of a classical problem has a solution without any restrictions on…

Higher order derivative theories, generally suffer from instabilities, known as Ostrogradsky instabilities. This issue can be resolved by removing any existing degeneracy present in such theories. We consider a model involving at most…

We prove Euler-Lagrange and natural boundary necessary optimality conditions for fractional problems of the calculus of variations which are given by a composition of functionals. Our approach uses the recent notions of Riemann-Liouville…

If a Lagrangian defining a variational problem has order $k$ then its Euler-Lagrange equations generically have order $2k$. This paper considers the case where the Euler-Lagrange equations have order strictly less than $2k$, and shows that…

We study more general variational problems on time scales. Previous results are generalized by proving necessary optimality conditions for (i) variational problems involving delta derivatives of more than the first order, and (ii) problems…

Let us consider the autonomous obstacle problem \begin{equation*} \min_v \int_\Omega F(Dv(x)) \, dx \end{equation*} on a specific class of admissible functions, where we suppose the Lagrangian satisfies proper hypotheses of convexity and…