Search results for "35"

A remark on infinite initial values for quasilinear parabolic equations

2020

Abstract We study the possibility of prescribing infinite initial values for solutions of the Evolutionary p -Laplace Equation in the fast diffusion case p > 2 . This expository note has been extracted from our previous work. When infinite values are prescribed on the whole initial surface, such solutions can exist only if the domain is a space–time cylinder.

Polarization tensors of planar domains as functions of the admittivity contrast

2014

(Electric) polarization tensors describe part of the leading order term of asymptotic voltage perturbations caused by low volume fraction inhomogeneities of the electrical properties of a medium. They depend on the geometry of the support of the inhomogeneities and on their admittivity contrast. Corresponding asymptotic formulas are of particular interest in the design of reconstruction algorithms for determining the locations and the material properties of inhomogeneities inside a body from measurements of current flows and associated voltage potentials on the body's surface. In this work we consider the two-dimensional case only and provide an analytic representation of the polarization t…

Compact embeddings and indefinite semilinear elliptic problems

2002

Our purpose is to find positive solutions $u \in D^{1,2}(\rz^N)$ of the semilinear elliptic problem $-\laplace u = h(x) u^{p-1}$ for $2<p$. The function $h$ may have an indefinite sign. Key ingredients are a $h$-dependent concentration-compactness Lemma and a characterization of compact embeddings of $D^{1,2}(\rz^N)$ into weighted Lebesgue spaces.

Lentigo Maligna:Un Approccio Concreto

2008

Anisotropic elliptic equations with gradient-dependent lower order terms and L^1 data

2023

&lt;abstract&gt;&lt;p&gt;We prove the existence of a weak solution for a general class of Dirichlet anisotropic elliptic problems such as $ \mathcal Au+\Phi(x, u, \nabla u) = \mathfrak{B}u+f $ in $ \Omega $, where $ \Omega $ is a bounded open subset of $ \mathbb R^N $ and $ f\in L^1(\Omega) $ is arbitrary. The principal part is a divergence-form nonlinear anisotropic operator $ \mathcal A $, the prototype of which is $ \mathcal A u = -\sum_{j = 1}^N \partial_j(|\partial_j u|^{p_j-2}\partial_j u) $ with $ p_j &amp;gt; 1 $ for all $ 1\leq j\leq N $ and $ \sum_{j = 1}^N (1/p_j) &amp;gt; 1 $. As a novelty in this paper, our lower order terms involve a new class of operators $ \mathfrak B $ such…

Home Country Institutions and Outward FDI: An Exploratory Analysis in Emerging Economies

2020

Although the internationalization of economies is driven by specific industry conditions or business-specific differences, the institutions that exist as background conditions directly determine firms&rsquo

Lichen planus orale

2009

Linfedema-Elefantiasi

2009

Humilde rogativa : con que los niños de las escuelas de Valencia imploran el patrocinio de sus patricios San Vicente Ferrer, San Luis Bertran, San Pe…

2 Grav. xil. precedeixen al tít Text a 1 col Sign.: [ ]2

Local uniqueness of the solutions for a singularly perturbed nonlinear nonautonomous transmission problem

2020

Abstract We consider the Laplace equation in a domain of R n , n ≥ 3 , with a small inclusion of size ϵ . On the boundary of the inclusion we define a nonlinear nonautonomous transmission condition. For ϵ small enough one can prove that the problem has solutions. In this paper, we study the local uniqueness of such solutions.