On a priori estimates for positive solutions of a semilinear biharmonic equation in a ball
On a probabilistic interpretation of shape derivatives of Dirichlet groundstates with application to Fermion nodes
This paper considers Schrödinger operators, and presents a probabilistic interpretation of the variation (or shape derivative) of the Dirichlet groundstate energy when the associated domain is perturbed. This interpretation relies on the distribution on the boundary of a stopped random process with Feynman-Kac weights. Practical computations require in addition the explicit approximation of the normal derivative of the groundstate on the boundary. We then propose to use this formulation in the...
On a problem of lower limit in the study of nonresonance.
On a problem of lower limit in the study of nonresonance with Leray-Lions operator.
On a Purely ?Riemannian" Proof of the Structure and Dimension of the Unramified Moduli Space of a Compact Riemann Surface.
On a quasilinear elliptic equation and a Riemannian metric invariant under Möbius transformations.
On a quasilinear elliptic equation and a Riemannian metric invariant under Möbius transformations. (Summary).
On a quasilinear inverse boundary value problem.
On a reaction-diffusion system involving the critical exponent.
In this paper we study the existence and multiplicity of the nontrivial solutions for a given elliptic system with Dirichlet boundary conditions and critical nonlinearity.
On a real Monge-Ampère functional.
On a semilinear elliptic eigenvalue problem
We obtain a description of the spectrum and estimates for generalized positive solutions of -Δu = λ(f(x) + h(u)) in Ω, , where f(x) and h(u) satisfy minimal regularity assumptions.
On a semilinear elliptic equation in
We prove existence/nonexistence and uniqueness of positive entire solutions for some semilinear elliptic equations on the Hyperbolic space.
On a semilinear variational problem
We provide a detailed analysis of the minimizers of the functional , , subject to the constraint . This problem,e.g., describes the long-time behavior of the parabolic Anderson in probability theory or ground state solutions of a nonlinear Schrödinger equation. While existence can be proved with standard methods, we show that the usual uniqueness results obtained with PDE-methods can be considerably simplified by additional variational arguments. In addition, we investigate qualitative properties...
On a semilinear variational problem
We provide a detailed analysis of the minimizers of the functional , , subject to the constraint . This problem, e.g., describes the long-time behavior of the parabolic Anderson in probability theory or ground state solutions of a nonlinear Schrödinger equation. While existence can be proved with standard methods, we show that the usual uniqueness results obtained with PDE-methods can be considerably simplified by additional variational arguments. In addition, we investigate qualitative properties...
On a singular sublinear polyharmonic problem.
On a Singular Value Problem for the Fractional Laplacian on the Exterior of the Unit Ball
2000 Mathematics Subject Classification: Primary 26A33; Secondary 47G20, 31B05We study a singular value problem and the boundary Harnack principle for the fractional Laplacian on the exterior of the unit ball.
On a Solution of Degenerate Elliptic-parabolic Systems in Orlicz-Sobolev Spaces II.
On a Solution of Degenerate Elliptic-parabolic Systems in Orlicz-Sobolev Spaces I.
On a sub-supersolution method for the prescribed mean curvature problem
The paper is about a sub-supersolution method for the prescribed mean curvature problem. We formulate the problem as a variational inequality and propose appropriate concepts of sub- and supersolutions for such inequality. Existence and enclosure results for solutions and extremal solutions between sub- and supersolutions are established.
On a superconvergent finite element scheme for elliptic systems. II. Boundary conditions of Newton's or Neumann's type
A simple superconvergent scheme for the derivatives of finite element solution is presented, when linear triangular elements are employed to solve second order elliptic systems with boundary conditions of Newton’s or Neumann’s type. For bounded plane domains with smooth boundary the local -superconvergence of the derivatives in the -norm is proved. The paper is a direct continuations of [2], where an analogous problem with Dirichlet’s boundary conditions is treated.