Penalty method in design optimization of systems governed by a unilateral boundary value problem
Perimeter on Fractal sets.
Periodic homogenization of a non-coercive class of functionals.
Periodic Solutions of Asymptotically Linear Hamiltonian Systems.
Periodic solutions of quadratic lagrangian systems on -convex sets
Periodic stabilization for linear time-periodic ordinary differential equations
This paper studies the periodic feedback stabilization of the controlled linear time-periodic ordinary differential equation: ẏ(t) = A(t)y(t) + B(t)u(t), t ≥ 0, where [A(·), B(·)] is a T-periodic pair, i.e., A(·) ∈ L∞(ℝ+; ℝn×n) and B(·) ∈ L∞(ℝ+; ℝn×m) satisfy respectively A(t + T) = A(t) for a.e. t ≥ 0 and B(t + T) = B(t) for a.e. t ≥ 0. Two periodic stablization criteria for a T-period pair [A(·), B(·)] are established. One is an analytic criterion which is related to the transformation over time...
Perron's method and the method of relaxed limits for "unbounded" PDE in Hilbert spaces
We prove that Perron's method and the method of half-relaxed limits of Barles-Perthame works for the so called B-continuous viscosity solutions of a large class of fully nonlinear unbounded partial differential equations in Hilbert spaces. Perron's method extends the existence of B-continuous viscosity solutions to many new equations that are not of Bellman type. The method of half-relaxed limits allows limiting operations with viscosity solutions without any a priori estimates. Possible applications...
Perturbation analysis of the discrete Riccati equation
Perturbation of mixed variational problems. Application to mixed finite element methods
Perturbation theory of duality in vector nonconvex optimization via the abstract duality scheme
Perturbation theory of duality in vector optimization via the abstract duality scheme
Perturbations of variational inequalities and rate of convergence of solutions
Perturbed iterative algorithms with errors for completely generalized strongly nonlinear implicit quasivariational inclusions.
Perturbed optimization problems in Banach spaces
Perturbed three-step approximation process with errors for a generalized implicit nonlinear quasivariational inclusions.
Perturbing away singularities of Harmonic Maps.
Perturbing away singularity from area-minimizing hypercones.
P-Harmonic obstacle problems.
Phase field method for mean curvature flow with boundary constraints
This paper is concerned with the numerical approximation of mean curvature flow t → Ω(t) satisfying an additional inclusion-exclusion constraint Ω1 ⊂ Ω(t) ⊂ Ω2. Classical phase field model to approximate these evolving interfaces consists in solving the Allen-Cahn equation with Dirichlet boundary conditions. In this work, we introduce a new phase field model, which can be viewed as an Allen Cahn equation with a penalized double well potential. We first justify this method by a Γ-convergence result...
Phase field method for mean curvature flow with boundary constraints
This paper is concerned with the numerical approximation of mean curvature flow t → Ω(t) satisfying an additional inclusion-exclusion constraint Ω1 ⊂ Ω(t) ⊂ Ω2. Classical phase field model to approximate these evolving interfaces consists in solving the Allen-Cahn equation with Dirichlet boundary conditions. In this work, we introduce a new phase field model, which can be viewed as an Allen Cahn equation with a penalized double well potential. We first justify this method by a Γ-convergence result...