This short communication develops an existence result for a general non-linear parabolic equation. The method of proof comprises an application of the Newton's method combined with a proximal approach and a Banach fixed point theorem.

This article develops an existence result for a general class of non-linear parabolic partial differential equations. The results are based on standard tools of functional analysis and Sobolev spaces theory. As a key strategy for such a proof, we discretize in the time variable and show the related sequence obtained is uniformly bounded concerning a norm in an appropriate Sobolev space.

This short communication develops a theoretical result on the Sobolev space W 1,2 (Ω). More specifically, under the indicated hypotheses, we prove that a bounded sequence in such a space has a subsequence with the gradient converging almost everywhere to a measurable function.

This article develops duality principles applicable to originally non-convex primal variational formulations, including an exact penalization context. More specifically, as a first application, we establish a convex dual variational formulation for a non-linear Kirchhoff-Love plate model. In a subsequent section, we develop a dual variational formulation for a related exactly penalized functional. The results are obtained through basic tools of functional analysis, calculus of variations, duality and optimization theory in infinite dimensional spaces. We emphasize such convex dual formulations obtained may be applied to a large class of similar models in the calculus of variations.

This article develops a duality principle applicable to originally non-convex primal variational formulations. More specifically, as a first application, we establish a convex dual variational formulation for a non-linear Kirchhoff-Love plate model. The results are obtained through basic tools of functional analysis, calculus of variations, duality and optimization theory in infinite dimensional spaces. We emphasize such a convex dual formulation obtained may be applied to a large class of similar models in the calculus of variations.

This article develops a duality principle through a D.C. approach applicable to some originally non-convex primal variational formulations. More specifically, in a first step, we develop applications to a Ginzburg-Landau type equation. The results are obtained through basic tools of functional analysis, calculus of variations, duality and optimization theory in infinite dimensional spaces. It is worth emphasizing we have obtained a convex dual variational formulation which may be applied to a large class of similar models in the calculus of variations. Finally, in the last sections we present a numerical example and related software.

This article develops a duality principle through a D.C. approach applicable to some originally non-convex primal variational formulations. More specifically, in a first step, we develop applications to a Ginzburg-Landau type equation. The results are obtained through basic tools of functional analysis, calculus of variations, duality and optimization theory in infinite dimensional spaces. It is worth emphasizing we have obtained a convex dual variational formulation which may be applied to a large class of similar models in the calculus of variations. Finally, in the last sections we present a numerical example and related software.

This article develops a duality principle applicable to some originally non-convex primal variational formulations. More specifically, in a first step, we develop applications to a Ginzburg-Landau type equation. The results are obtained through basic tools of functional analysis, calculus of variations, duality and optimization theory in infinite dimensional spaces. It is worth emphasizing we have obtained a convex dual variational formulation which may be applied to a large class of similar models in the calculus of variations. Finally, in the last sections we present a numerical example and related software.

This article develops duality principles applicable to originally non-convex primal variational formulations. More specifically, as a first application, we establish a convex dual variational formulation for a non-linear model in elasticity. The results are obtained through basic tools of functional analysis, calculus of variations, duality and optimization theory in infinite dimensional spaces. We emphasize such a convex dual formulation obtained may be applied to a large class of similar models in the calculus of variations. In a subsequent section, we present a global existence result for such a concerning model in elasticity. Finally, in the last sections, we develop duality principles and relaxation procedures for a related model in phase transition.

This article develops a duality principle applicable to originally non-convex primal variational formulations. More specifically, we establish a convex (in fact concave) dual variational formulation for a model in micro-magnetism. The results are obtained through basic tools of functional analysis, calculus of variations, duality and optimization theory in infinite dimensional spaces. We emphasize such a convex dual formulation obtained may be applied to a large class of similar models in the calculus of variations, including models in elasticity and phase transition.

This article develops duality principles applicable to originally non-convex primal variational formulations. More specifically, as a first application, we establish a convex dual variational formulation for a non-linear model in elasticity. The results are obtained through basic tools of functional analysis, calculus of variations, duality and optimization theory in infinite dimensional spaces. We emphasize such a convex dual formulation obtained may be applied to a large class of similar models in the calculus of variations. In a subsequent section, we present a global existence result for such a concerning model in elasticity. Finally, in the last sections, we develop duality principles and relaxation procedures for a related model in phase transition.

This article develops a duality principle applicable to originally non-convex primal variational formulations. More specifically, as a first application, we establish a convex dual variational formulation for a non-linear model in elasticity. The results are obtained through basic tools of functional analysis, calculus of variations, duality and optimization theory in infinite dimensional spaces. We emphasize such a convex dual formulation obtained may be applied to a large class of similar models in the calculus of variations. Finally, in the last section, we present a global existence result for such a concerning model.