Search results for "dirichlet"
showing 10 items of 197 documents
(p,2)-equations resonant at any variational eigenvalue
2018
We consider nonlinear elliptic Dirichlet problems driven by the sum of a p-Laplacian and a Laplacian (a (p,2) -equation). The reaction term at ±∞ is resonant with respect to any variational eigenvalue of the p-Laplacian. We prove two multiplicity theorems for such equations.
Global representation and multiscale expansion for the Dirichlet problem in a domain with a small hole close to the boundary
2019
For each pair (Formula presented.) of positive parameters, we define a perforated domain (Formula presented.) by making a small hole of size (Formula presented.) in an open regular subset (Formula presented.) of (Formula presented.) ((Formula presented.)). The hole is situated at distance (Formula presented.) from the outer boundary (Formula presented.) of the domain. Thus, when (Formula presented.) both the size of the hole and its distance from (Formula presented.) tend to zero, but the size shrinks faster than the distance. Next, we consider a Dirichlet problem for the Laplace equation in the perforated domain (Formula presented.) and we denote its solution by (Formula presented.) Our ai…
Variational versus pseudomonotone operator approach in parameter-dependent nonlinear elliptic problems
2013
We study the existence of nontrivial solutions of parameter-dependent quasilinear elliptic Dirichlet problems of the form $-\Delta u = \lambda f(u)$ in $\Omega$, $u = 0$ on $\partial\Omega$, in a bounded domain $\Omega$ with sufficiently smooth boundary, where $\lambda$ is a real parameter and $\Delta_p$ denotes the p-Laplacian. Recently the authors obtained multiplicity results by employing an abstract localization principle of critical points of functional of the form $\Phi-\lambda\Psi$ on open subleveis of $\Phi$, i.e., of sets of the form $\Phi^{-1}(-\infty,r)$, combined with differential inequality techniques and topological arguments. Unlike in those recent papers by the authors, the …
Gradient nonlinear elliptic systems driven by a (p,q)-laplacian operator
2017
In this paper, using variational methods and critical point theorems, we prove the existence of multiple weak solutions for a gradient nonlinear Dirichlet elliptic system driven by a (p, q)-Laplacian operator.
Existence of positive solutions for nonlinear Dirichlet problems with gradient dependence and arbitrary growth
2018
We consider a nonlinear elliptic problem driven by the Dirichlet $p$-Laplacian and a reaction term which depends also on the gradient (convection). No growth condition is imposed on the reaction term $f(z, \cdot,y)$. Using topological tools and the asymptotic analysis of a family of perturbed problems, we prove the existence of a positive smooth solution.
Applications of Microlocal Analysis in Inverse Problems
2020
This note reviews certain classical applications of microlocal analysis in inverse problems. The text is based on lecture notes for a postgraduate level minicourse on applications of microlocal analysis in inverse problems, given in Helsinki and Shanghai in June 2019.
A two-stage LDA algorithm for ranking induced topic readability
2022
Probabilistic topic models, such as LDA, are standard text analysis algorithms that provide predictive and latent topic representation for a corpus. However, due to the unsupervised training process, it is difficult to verify the assumption that the latent space discovered by these models is generally meaningful and valuable. This paper introduces a two-stage LDA algorithm to estimate latent topics in text documents and use readability scores to link the identified topics to a linguistically motivated latent structure. We define a new interpretative tool called induced topic readability, which is used to rank topics from the one with the most complex linguistic structure to the one with the…
Organizational identity and competition : a study of US semiconductor industry
2017
Organisationaalinen identiteetti ja kilpailu : tutkielma puolijohdeteollisuudesta. Tutkimuksen tehtävänä on selvittää, miten kaksi samalla puolijohdesektorilla kilpailevaa yritystä, Intel Corporation ja Advanced Micro Devices, kuvailee itseänsä ja kenttäänsä suhteessa kilpailijoihinsa ja siten rakentaa ja ylläpitää organisationaalista identiteettiään. Tutkimuksen teoreettisena näkökulmana on tarkastella markkinoita sosiaalisesti rakentuneena kenttänä jota kilpailu ylläpitää. Analyysimenetelmänä on käytetty koneoppivaa tekstin mallinnusmenetelmää nimeltä Latentti Dirichlet Allokaatio (LDA), jolla …
On the Sub-Supersolution Approach for Dirichlet Problems driven by a (p(x), q(x))-Laplacian Operator with Convection Term
2021
The method of sub and super-solution is applied to obtain existence and location of solutions to a quasilinear elliptic problem with variable exponent and Dirichlet boundary conditions involving a nonlinear term f depending on solution and on its gradient. Under a suitable growth condition on the convection term f, the existence of at least one solution satisfying a priori estimate is obtained.
A Continuous Approach to FETI-DP Mortar Methods: Application to Dirichlet and Stokes Problem
2013
In this contribution we extend the FETI-DP mortar method for elliptic problems introduced by Bernardi et al. [2] and Chacon Vera [3] to the case of the incompressible Stokes equations showing that the same results hold in the two dimensional setting. These ideas extend easily to three dimensional problems. Finally some numerical tests are shown as a conclusion. This contribution is a condensed version of a more detailed forthcoming paper. We use standard notation, see for instance [1].