Search results for "value"

Superconductive and insulating inclusions for linear and non-linear conductivity equations

2015

We detect an inclusion with infinite conductivity from boundary measurements represented by the Dirichlet-to-Neumann map for the conductivity equation. We use both the enclosure method and the probe method. We use the enclosure method to prove partial results when the underlying equation is the quasilinear $p$-Laplace equation. Further, we rigorously treat the forward problem for the partial differential equation $\operatorname{div}(\sigma\lvert\nabla u\rvert^{p-2}\nabla u)=0$ where the measurable conductivity $\sigma\colon\Omega\to[0,\infty]$ is zero or infinity in large sets and $1<p<\infty$.

Poincaré Type Inequalities for Vector Functions with Zero Mean Normal Traces on the Boundary and Applications to Interpolation Methods

2018

We consider inequalities of the Poincare–Steklov type for subspaces of \(H^1\)-functions defined in a bounded domain \(\varOmega \in \mathbb {R}^d\) with Lipschitz boundary \(\partial \varOmega \). For scalar valued functions, the subspaces are defined by zero mean condition on \(\partial \varOmega \) or on a part of \(\partial \varOmega \) having positive \(d-1\) measure. For vector valued functions, zero mean conditions are applied to normal components on plane faces of \(\partial \varOmega \) (or to averaged normal components on curvilinear faces). We find explicit and simply computable bounds of constants in the respective Poincare type inequalities for domains typically used in finite …

Comments on the validity of a common category of constitutive equations

1974

Many constitutive equations for viscoelastic materials which have appeared in the literature are modifications of the linear viscoelasticity model. Their general form is: [5] $$\tau = \int\limits_0^\infty {(f_1 C + f_2 C^{ - 1)} ds.} $$ The memory functionsf 1 andf 2, are assumed to depend explicitly on either some instantaneous or some timeaveraged value of the invariants of the rate of strain. It is shown in this paper that the general theory of simple fluids with fading memory is based on certain assumptions of smoothness for the constitutive functional which are violated by constitutive equations of the type discussed. This implies that, should any real material obey eq. [5], with an ex…

Bounds for the first Dirichlet eigenvalue of domains in Kaehler manifolds

1991

The Lang–Vojta Conjectures on Projective Pseudo-Hyperbolic Varieties

2020

These notes grew out of a mini-course given from May 13th to May 17th at UQAM in Montreal during a workshop on Diophantine Approximation and Value Distribution Theory.

OBSTACLE PROBLEMS FOR DEGENERATE ELLIPTIC EQUATIONS WITH NONHOMOGENEOUS NONLINEAR BOUNDARY CONDITIONS

2008

In this paper we study the questions of existence and uniqueness of solutions for equations of type - div a(x,Du) + γ(u) ∋ ϕ, posed in an open bounded subset Ω of ℝN, with nonlinear boundary conditions of the form a(x,Du) · η + β(u) ∋ ψ. The nonlinear elliptic operator div a(x,Du) modeled on the p-Laplacian operator Δp(u) = div (|Du|p-2Du), with p &gt; 1, γ and β maximal monotone graphs in ℝ2 such that 0 ∈ γ(0) ∩ β(0), [Formula: see text] and the data ϕ ∈ L1(Ω) and ψ ∈ L1(∂ Ω). Since D(γ) ≠ ℝ, we are dealing with obstacle problems. For this kind of problems the existence of weak solution, in the usual sense, fails to be true for nonhomogeneous boundary conditions, so a new concept of solut…

A fuzzification of the category of M-valued L-topological spaces

2004

[EN] A fuzzy category is a certain superstructure over an ordinary category in which ”potential” objects and ”potential” morphisms could be such to a certain degree. The aim of this paper is to introduce a fuzzy category FTOP(L,M) extending the category TOP(L,M) of M-valued L- topological spaces which in its turn is an extension of the category TOP(L) of L-fuzzy topological spaces in Kubiak-Sostak’s sense. Basic properties of the fuzzy category FTOP(L,M) and its objects are studied.

The Second Main Theorem

1998

Actions de IR et courbure de ricci du Fibré unitaire tangent des surfaces

1986

Characterisation of 2-dimensional Riemannian manifolds (M, g) (in particular, of surfaces with constant gaussian curvatureK=1/c2, o,−1/c2, respectively) whose tangent circle bundle (TcM, gs) (gs=Sasaki metric) admit an «almost-regular» vector field belonging to an eigenspace of the Ricci operator.

Multidimensional Borg–Levinson theorems for unbounded potentials

2018

We prove that the Dirichlet eigenvalues and Neumann boundary data of the corresponding eigenfunctions of the operator $-\Delta + q$, determine the potential $q$, when $q \in L^{n/2}(\Omega,\mathbb{R})$ and $n \geq 3$. We also consider the case of incomplete spectral data, in the sense that the above spectral data is unknown for some finite number of eigenvalues. In this case we prove that the potential $q$ is uniquely determined for $q \in L^p(\Omega,\mathbb{R})$ with $p=n/2$, for $n\geq4$ and $p>n/2$, for $n=3$.