177,077 research outputs found
Asymptotics for a high-energy solution of a supercritical problem
No full textIn this paper we deal with the equation
for , under Neumann boundary conditions in the unit ball of
. We focus on the three positive, radial, and radially
non-decreasing solutions, whose existence for large is proved in [13]. We
detect the limit profile as of the higher energy solution and show
that, unlike the minimal energy one, it converges to the constant . The
proof requires several tools borrowed from the theory of minimization problems
and accurate a priori estimates of the solutions, which are of independent
interest.Comment: 14 pages, revised versio
The Soap Bubble Theorem and a -Laplacian overdetermined problem
No full textWe consider the p-Laplacian equation -Delta(p)u = 1 for 1 < p < 2, on a regular bounded domain Omega subset of R-N, with N >= 2, under homogeneous Dirichlet boundary conditions. In the spirit of Alexandrov's Soap Bubble Theorem and of Serrin's symmetry result for the overdetermined problems, we prove that if the mean curvature H of partial derivative Omega is constant, then Omega is a ball and the unique solution of the Dirichlet p-Laplacian problem is radial. The main tools used are integral identities, the P-function, and the maximum principle
Upper and Lower Motor Neurons and the Skeletal Muscle: Implication for Amyotrophic Lateral Sclerosis (ALS)
No full textThe relationships between motor neurons and the skeletal muscle during development and in pathologic contexts are addressed in this Chapter.We discuss the developmental interplay of muscle and nervous tissue, through neurotrophins and the activation of differentiation and survival pathways. After a brief overview on muscular regulatory factors, we focus on the contribution of muscle to early and late neurodevelopment. Such a role seems especially intriguing in relation to the epigenetic shaping of developing motor neuron fate choices. In this context, emphasis is attributed to factors regulating energy metabolism, which may concomitantly act in muscle and neural cells, being involved in common pathways.We then review the main features of motor neuron diseases, addressing the cellular processes underlying clinical symptoms. The involvement of different muscle-associated neurotrophic factors for survival of lateral motor column neurons, innervating MyoD-dependent limb muscles, and of medial motor column neurons, innervating Myf5-dependent back musculature is discussed. Among the pathogenic mechanisms, we focus on oxidative stress, that represents a common and early trait in several neurodegenerative disorders. The role of organelles primarily involved in reactive oxygen species scavenging and, more generally, in energy metabolism-namely mitochondria and peroxisomes-is discussed in the frame of motor neuron degeneration.We finally address muscular involvement in amyotrophic lateral sclerosis (ALS), a multifactorial degenerative disorder, hallmarked by severe weight loss, caused by imbalanced lipid metabolism. Even though multiple mechanisms have been recognized to play a role in the disease, current literature generally assumes that the primum movens is neuronal degeneration and that muscle atrophy is only a consequence of such pathogenic event. However, several lines of evidence point to the muscle as primarily involved in the disease, mainly through its role in energy homeostasis. Data from different ALS mouse models strongly argue for an early mitochondrial dysfunction in muscle tissue, possibly leading to motor neuron disturbances. Detailed understanding of skeletal muscle contribution to ALS pathogenesis will likely lead to the identification of novel therapeutic strategies
Upper and Lower Motor Neurons and the Skeletal Muscle: Implication for Amyotrophic Lateral Sclerosis (ALS).
No full textThe relationships between motor neurons and the skeletal muscle during development and in pathologic contexts are addressed in this Chapter.We discuss the developmental interplay of muscle and nervous tissue, through neurotrophins and the activation of differentiation and survival pathways. After a brief overview on muscular regulatory factors, we focus on the contribution of muscle to early and late neurodevelopment. Such a role seems especially intriguing in relation to the epigenetic shaping of developing motor neuron fate choices. In this context, emphasis is attributed to factors regulating energy metabolism, which may concomitantly act in muscle and neural cells, being involved in common pathways. We then review the main features of motor neuron diseases, addressing the cellular processes underlying clinical symptoms. The involvement of different muscle-associated neurotrophic factors for survival of lateral motor column neurons, innervating MyoD-dependent limb muscles, and of medial motor column neurons, innervating Myf5-dependent back musculature is discussed. Among the pathogenic mechanisms, we focus on oxidative stress, that represents a common and early trait in several neurodegenerative disorders. The role of organelles primarily involved in reactive oxygen species scavenging and, more generally, in energy metabolism-namely mitochondria and peroxisomes-is discussed in the frame of motor neuron degeneration. We finally address muscular involvement in amyotrophic lateral sclerosis (ALS), a multifactorial degenerative disorder, hallmarked by severe weight loss, caused by imbalanced lipid metabolism. Even though multiple mechanisms have been recognized to play a role in the disease, current literature generally assumes that the primum movens is neuronal degeneration and that muscle atrophy is only a consequence of such pathogenic event. However, several lines of evidence point to the muscle as primarily involved in the disease, mainly through its role in energy homeostasis. Data from different ALS mouse models strongly argue for an early mitochondrial dysfunction in muscle tissue, possibly leading to motor neuron disturbances. Detailed understanding of skeletal muscle contribution to ALS pathogenesis will likely lead to the identification of novel therapeutic strategies
The treatment of infantile coxa vara with the external circular fixator.
No full textCoxa vara worsens as it evolves, and is often accompanied by other femoral deformities, such as hypometria, axial knee deviations, and rotational deformity. Traditional surgical techniques, especially intracapsular femoral neck osteotomy, are difficult to execute and often cause joint stiffness while not sufficiently correcting the coxa vara or the other deformities, in particular hypometria. For these reasons this study used the external circular fixator to simultaneously correct these deformities. The results are presented after discussion of technical detail
Multiplicity of Solutions on a Nehari Set in an Invariant Cone
No full textFor 1<2 and large, we prove the existence of two positive, nonconstant, radial and radially nondecreasing solutions of the supercritical equation
under Neumann boundary conditions, in the unit ball of .
We use a variational approach in an invariant cone. We distinguish the two solutions upon their energy: one is a ground state inside a Nehari-type subset of the cone, the other is obtained via a mountain pass argument inside the Nehari set.
As a byproduct of our proofs, we detect the limit profile of the low energy solution as and show that the constant solution 1 is a local minimizer on the Nehari set. This marks a strong difference with the case
Multiplicity of solutions on a Nehari set in an invariant cone
No full textFor 1 < p < 2 and q large, we prove the existence of two positive, nonconstant, radial and radially nondecreasing solutions of the supercritical equation −∆pu + u^p−1 = u^q−1 under Neumann boundary conditions, in the unit ball of R^N. We use a variational approach in an invariant cone. We distinguish the two solutions upon their energy: one is a ground state inside a Nehari-type subset of the cone, the other is obtained via a mountain pass argument inside the Nehari set. As a byproduct of our proofs, we detect the limit profile of the low energy solution as q → ∞ and show that the constant solution 1 is a local minimizer on the Nehari set. This marks a strong difference with the case p ≥ 2
On the Born–Infeld equation for electrostatic fields with a superposition of point charges
No full textIn this paper, we study the static Born–Infeld equation -div(∇u1-|∇u|2)=∑k=1nakδxkinRN,lim|x|→∞u(x)=0,where N≥ 3 , ak∈ R for all k= 1 , ⋯ , n, xk∈ RN are the positions of the point charges, possibly non-symmetrically distributed, and δxk is the Dirac delta distribution centered at xk. For this problem, we give explicit quantitative sufficient conditions on ak and xk to guarantee that the minimizer of the energy functional associated with the problem solves the associated Euler–Lagrange equation. Furthermore, we provide a more rigorous proof of some previous results on the nature of the singularities of the minimizer at the points xk’s depending on the sign of charges ak’s. For every m∈ N, we also consider the approximated problem -∑h=1mαhΔ2hu=∑k=1nakδxkinRN,lim|x|→∞u(x)=0where the differential operator is replaced by its Taylor expansion of order 2m (see (2.1)). It is known that each of these problems has a unique solution. We study the regularity of the approximating solution, the nature of its singularities, and the asymptotic behavior of the solution and of its gradient near the singularities
On Arabic, religion and non-Arab descent: the case of al-Zamaḫšarī
No full textThis paper intends to offer a close reading and a few remarks on selected texts useful to give an insight into al-Zamaḫšarī’s view of Arabic and Arabic grammar in terms of identitarian and ideological construct. Considering the amount of scholarly literature available on al-Kaššāf, the paper focuses on the introduction to al-Mufaṣṣal fī ṣanʿat al-iʿrāb (The Detailed [Presentation] of the Art of Clear Speech, putting it in conversation with the introductions of Muqaddimat al-Adab (Introduction to Belles-Lettres), and Asrār al-balāġa (The secrets of eloquence, a dictionary of tropes) to show how al-Zamaḫšarī’s approach to Arabic exemplifies the deep interconnection between language, religion, and (ethnic) identity in the Arabic intellectual traditio
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