1,721,012 research outputs found
Existence Theorems in the Calculus of Variations
No full textMascolo, E.; Schianchi, R.. (1984). Existence Theorems in the Calculus of Variations. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/2247
Gradient regularity for minimizers of functionals under p-q subquadratic growth
No full textWe prove higher integrability of the gradient for minimizers of functional with p-q subquadratic growth
The genetics of diabetes: What we can learn from Drosophila
Full text linkDiabetes mellitus is a heterogeneous disease characterized by hyperglycemia due to impaired insulin secretion and/or action. All diabetes types have a strong genetic component. The most frequent forms, type 1 diabetes (T1D), type 2 diabetes (T2D) and gestational diabetes mellitus (GDM), are multifactorial syndromes associated with several genes’ effects together with environmental factors. Conversely, rare forms, neonatal diabetes mellitus (NDM) and maturity onset diabetes of the young (MODY), are caused by mutations in single genes. Large scale genome screenings led to the identification of hundreds of putative causative genes for multigenic diabetes, but all the loci identified so far explain only a small proportion of heritability. Nevertheless, several recent studies allowed not only the identification of some genes as causative, but also as putative targets of new drugs. Although monogenic forms of diabetes are the most suited to perform a precision approach and allow an accurate diagnosis, at least 80% of all monogenic cases remain still undiag-nosed. The knowledge acquired so far addresses the future work towards a study more focused on the identification of diabetes causal variants; this aim will be reached only by combining expertise from different areas. In this perspective, model organism research is crucial. This review traces an overview of the genetics of diabetes and mainly focuses on Drosophila as a model system, describing how flies can contribute to diabetes knowledge advancement
Local boundedness for solutions of a class of nonlinear elliptic systems
Full text linkIn this paper we are concerned with the regularity of solutions to a nonlinear elliptic system of m equations in divergence form, satisfying p growth from below and q growth from above, with p≤ q; this case is known as p, q-growth conditions. Well known counterexamples, even in the simpler case p= q, show that solutions to systems may be singular; so, it is necessary to add suitable structure conditions on the system that force solutions to be regular. Here we obtain local boundedness of solutions under a componentwise coercivity condition. Our result is obtained by proving that each component uα of the solution u= (u1,.. , um) satisfies an improved Caccioppoli’s inequality and we get the boundedness of uα by applying De Giorgi’s iteration method, provided the two exponents p and q are not too far apart. Let us remark that, in dimension n= 3 and when p= q, our result works for 3/
Existence of weak solutions for elliptic systems with p,q-growth
No full textWe consider nonlinear systems in divergence form with p,q-growth. We prove existence of weak solutions provided p and q are close enough and under suitable summability assumptions on the boundary datum
Regularity of quasi-minimizers for non-uniformly elliptic integrals
Full text linkIn this paper we consider a class of non-uniformly elliptic integral functionals and we prove the local boundedness of the quasi-minimizers. Our approach is based on a suitable adaptation of the celebrated De Giorgi proof, and it relies on an appropriate Caccioppoli-type inequality
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