On the numerical solution of the first biharmonic equation
On the numerical solutions of convection-diffusion equations
On the optimal control of coefficients in elliptic problems. Application to the optimization of the head slider
We consider an optimal control problem for a class of non-linear elliptic equations. A result of existence and uniqueness of the state equation is proven under weaker hypotheses than in the literature. We also prove the existence of an optimal control. Applications to some lubrication problems and numerical results are given.
On the optimal control of coefficients in elliptic problems. Application to the optimization of the head slider
We consider an optimal control problem for a class of non-linear elliptic equations. A result of existence and uniqueness of the state equation is proven under weaker hypotheses than in the literature. We also prove the existence of an optimal control. Applications to some lubrication problems and numerical results are given.
On the optimal control of nonresonant elliptic equations
On the optimal growth of functions with bounded Laplacian.
On the oscillation of forced second order mixed-nonlinear elliptic equations
Oscillation theorems are established for forced second order mixed-nonlinear elliptic differential equations ⎧ , ⎨ ⎩ under quite general conditions. These results are extensions of the recent results of Sun and Wong, [J. Math. Anal. Appl. 334 (2007)] and Zheng, Wang and Han [Appl. Math. Lett. 22 (2009)] for forced second order ordinary differential equations with...
On the -growth of entire function solutions of Helmholtz equation.
On the PC-ansatz.
On the penalized obstacle problem in the unit half ball.
On the point spectrum of Schrödinger operators
On the principal eigencurve of the p-Laplacian related to the Sobolev trace embedding
We prove that for any λ ∈ ℝ, there is an increasing sequence of eigenvalues μₙ(λ) for the nonlinear boundary value problem ⎧ in Ω, ⎨ ⎩ on crtial ∂Ω and we show that the first one μ₁(λ) is simple and isolated; we also prove some results about variations of the density ϱ and the continuity with respect to the parameter λ.
On the Principal Eigenvalue of a Second Order Linear Elliptic Problem with an Indefinite Weight Function.
On the principal eigenvalue of elliptic operators in and applications
Two generalizations of the notion of principal eigenvalue for elliptic operators in are examined in this paper. We prove several results comparing these two eigenvalues in various settings: general operators in dimension one; self-adjoint operators; and “limit periodic” operators. These results apply to questions of existence and uniqueness for some semilinear problems in the whole space. We also indicate several outstanding open problems and formulate some conjectures.
On the Principal Eigenvalues of Indefinite Elliptic Problems.
On the problem of convergence of a bounded-below sequence of symmetric forms for the Schrödinger operators
On the properties of infinity-harmonic functions and an application to capacitary convex rings.
On the quasi-classical asymptotics of the forward scattering amplitude and of the total scattering cross-section
On the quasi-classical limit of the total scattering cross-section in nonrelativistic quantum mechanics
On the quasiuniqueness of solutions of degenerate equations in Hilbert space.