Elliptic grids with nearly uniform cell area and line spacing.
Elliptic perturbations for Hammerstein equations with singular nonlinear term.
Elliptic problems in generalized Orlicz-Musielak spaces
We consider a strongly nonlinear monotone elliptic problem in generalized Orlicz-Musielak spaces. We assume neither a Δ2 nor ∇2-condition for an inhomogeneous and anisotropic N-function but assume it to be log-Hölder continuous with respect to x. We show the existence of weak solutions to the zero Dirichlet boundary value problem. Within the proof the L ∞-truncation method is coupled with a special version of the Minty-Browder trick for non-reflexive and non-separable Banach spaces.
Elliptic problems with integral diffusion
In this paper, we review several recent results dealing with elliptic equations with non local diffusion. More precisely, we investigate several problems involving the fractional laplacian. Finally, we present a conformally covariant operator and the associated singular and regular Yamabe problem.
Elliptic problems with nonmonotone discontinuities at resonance.
Elliptic quasi-variational inequalities and application to a non-stationary problem in hydraulics
Elliptic regularity and essential self-adjointness of Dirichlet operators on
Elliptic resonance problems with unequal limits at infinity.
Elliptische Differentialgleichungen mit variablen Koeffizienten in Gebieten mit unbeschränktem Rand.
Embedded eigenvalues and resonances of Schrödinger operators with two channels
In this article, we give a necessary and sufficient condition in the perturbation regime on the existence of eigenvalues embedded between two thresholds. For an eigenvalue of the unperturbed operator embedded at a threshold, we prove that it can produce both discrete eigenvalues and resonances. The locations of the eigenvalues and resonances are given.
Embedding and a priori wavelet-adaptivity for Dirichlet problems
Embedding and a priori wavelet-adaptivity for Dirichlet problems
The accuracy of the domain embedding method from [A. Rieder, Modél. Math. Anal. Numér.32 (1998) 405-431] for the solution of Dirichlet problems suffers under a coarse boundary approximation. To overcome this drawback the method is furnished with an a priori (static) strategy for an adaptive approximation space refinement near the boundary. This is done by selecting suitable wavelet subspaces. Error estimates and numerical experiments validate the proposed adaptive scheme. In contrast to similar,...
Embedding of open riemannian manifolds by harmonic functions
Let be a noncompact Riemannian manifold of dimension . Then there exists a proper embedding of into by harmonic functions on . It is easy to find harmonic functions which give an embedding. However, it is more difficult to achieve properness. The proof depends on the theorems of Lax-Malgrange and Aronszajn-Cordes in the theory of elliptic equations.
Embedding theorems into lipschitz and BMO spaces and applications to quasilinear subelliptic differential equations.
En ε-uniformly convergent non-conforming finite element method for a singularly perturbed elliptic problem in two dimensions
Enclosure of solutions for elliptic boundary value problems with nonmonotone discontinuous nonlinearity
Energies of -valued harmonic maps on polyhedra with tangent boundary conditions
Énergies relaxées pour applications harmoniques
Energy and Morse index of solutions of Yamabe type problems on thin annuli
We consider the Yamabe type family of problems , in , on , where is an annulus-shaped domain of , , which becomes thinner as . We show that for every solution , the energy as well as the Morse index tend to infinity as . This is proved through a fine blow up analysis of appropriate scalings of solutions whose limiting profiles are regular, as well as of singular solutions of some elliptic problem on , a half-space or an infinite strip. Our argument also involves a Liouville type theorem...
Energy quantization and mean value inequalities for nonlinear boundary value problems
We give a unified statement and proof of a class of well known mean value inequalities for nonnegative functions with a nonlinear bound on the Laplacian. We generalize these to domains with boundary, requiring a (possibly nonlinear) bound on the normal derivative at the boundary. These inequalities give rise to an energy quantization principle for sequences of solutions of boundary value problems that have bounded energy and whose energy densities satisfy nonlinear bounds on the Laplacian and normal...