A semi-linear elliptic equation in a strip arising in a two-dimensional flame propagation model.
A semilinear elliptic problem involving nonlinear boundary condition and sign-changing potential.
A semi-linear problem for the Heisenberg laplacian
A singular equation with positive and free boundary solutions.
Para 0 < β < 1 consideramos la ecuación -Δu = χ{u > 0} (-u-β + λf(x, u)) en Ω con condición de borde tipo Dirichlet. Esta ecuación posee una solución maximal uλ ≥ 0 para todo λ > 0. Si λ es menor que una cierta constante λ*, uλ se anula en el interior del dominio creando una frontera libre, y para λ > λ* esta solución es positiva en Ω y estable. Establecemos la regularidad de uλ incluso en presencia de una frontera libre. Para λ ≥ λ* la solución del problema...
A singular Gierer—Meinhardt system of elliptic equations
A stochastic impulse control problem with quadratic growth Hamiltonian and the corresponding quasi variational inequality.
A strongly nonlinear problem arising in glaciology
A strongly nonlinear problem arising in glaciology
The computation of glacier movements leads to a system of nonlinear partial differential equations. The existence and uniqueness of a weak solution is established by using the calculus of variations. A discretization by the finite element method is done. The solution of the discrete problem is proved to be convergent to the exact solution. A first simple numerical algorithm is proposed and its convergence numerically studied.
A subsolution-supersolution method for quasilinear systems.
A Theorem on Elliptic Differential Inequalities with an Application to Gradient Bounds.
A two parameters Ambrosetti-Prodi problem.
A two-step Monge-Ampère procedure for solving a fourth order PDE for affine hypersurfaces with constant curvature.
A unique continuation property for linear elliptic systems and nonresonance problems.
A Uniqueness Theorem for Some Nonlinear Boundary Value Problems with a Large Parameter.
A variational solution of the A. D. Aleksandrov problem of existence of a convex polytope with prescribed Gauss curvature
In his book on convex polytopes [2] A. D. Aleksandrov raised a general question of finding variational formulations and solutions to geometric problems of existence of convex polytopes in , n ≥ 2, with prescribed geometric data. Examples of such problems for closed convex polytopes for which variational solutions are known are the celebrated Minkowski problem [2] and the Gauss curvature problem [20]. In this paper we give a simple variational proof of existence for the A. D. Aleksandrov problem...
A variational treatment for general elliptic equations of the flame propagation type : regularity of the free boundary
A W1,p-Estimate for Solutions to Mixed Boundary Value Problems for Second Order Elliptic Differential Equtions.
A weak maximum principle and estimates of for nonlinear degenerate elliptic equations
About Uniqueness for Nonlinear Boundary Value Problems.
Adaptive coupling of boundary elements and finite elements