Papers by Gioconda Moscariello
Atti della Accademia nazionale dei Lincei, Nov 26, 2023
Calculus of variations and partial differential equations, Apr 4, 2024
We consider local solutions u of nonlinear elliptic systems of the type div A(x, Du) = div F in ⊂... more We consider local solutions u of nonlinear elliptic systems of the type div A(x, Du) = div F in ⊂ R n , where u : → R N is in a weighted W 1, p loc space, with p ≥ 2, F is in a weighted W 1,2 loc space and x → A(x, ξ) has growth coefficients in the space of functions with bounded mean oscillation. We prove higher differentiability of u in the sense that the nonlinear expression of its gradient V μ (Du) := (μ 2 + |Du| 2) p−2 4 Du, with 0 < μ ≤ 1, is weakly differentiable with D(V μ (Du)) in a weighted L 2 loc space. Moreover we derive some local Calderón-Zygmund estimates when the source term is not necessarily differentiable. Global estimates for a suitable Dirichlet problem are also available.
From the 'geometric function theory' part of the title, a generic browser would probably expect t... more From the 'geometric function theory' part of the title, a generic browser would probably expect to find in this book a discussion on the coefficient estimates for univalent functions. The contents of this monograph are, however, far removed from this topic, and a quick leafing-through should soon convince the reader that the authors consider geometric function theory to be a very broad subject. To quote them: 'This book is largely about geometry of mappings-that is, functions or deformations between subsets of the Euclidean n-space and more generally between manifolds or other geometric objects.' The book begins with a massive, 31-page-long introduction and overview that concentrates on the central results of the theory of mappings of bounded distortion, also called 'quasiregular mappings', and on the connections with and applications to other fields of this theory. This is an expertly written overview, which will be of value even to specialists in the field. What, then, is a mapping of bounded distortion, or a quasiregular mapping? Consider a deformation f of a three-dimensional elastic body. It is often reasonable to expect that the infinitesimal behaviour will be similar in all directions-that is, that the quantity lim sup r→0 max{|f(x) − f(y)| : |x − y| = r} min{|f(x) − f(y)| : |x − y| = r}
arXiv (Cornell University), Dec 11, 2013
We study the Dirichlet problem for a p-Laplacian type operator in the setting of the Orlicz-Zygmu... more We study the Dirichlet problem for a p-Laplacian type operator in the setting of the Orlicz-Zygmund space L q log −α L (Ω, R n), q > 1 and α > 0. More precisely, our aim is to establish which assuptions on the parameter α > 0 lead to existence, uniqueness of the solution and continuity of the associated nonlinear operator.
Mathematics in Engineering
We investigate the obstacle problem for a class of nonlinear and noncoercive parabolic variationa... more We investigate the obstacle problem for a class of nonlinear and noncoercive parabolic variational inequalities whose model is a Leray–Lions type operator having singularities in the coefficients of the lower order terms. We prove the existence of a solution to the obstacle problem satisfying a Lewy-Stampacchia type inequality.
Advances in Nonlinear Analysis
We prove an existence result for obstacle problems related to convection-diffusion parabolic equa... more We prove an existence result for obstacle problems related to convection-diffusion parabolic equations with singular coefficients in the convective term. Our operator is not coercive, the obstacle function is time-dependent irregular, and the coefficients in the lower-order term belong to a borderline mixed Lebesgue-Marcinkiewicz space.
Abstract and Applied Analysis, 2015
We study the obstacle problem for second order nonlinear equations whose model appears in the sta... more We study the obstacle problem for second order nonlinear equations whose model appears in the stationary diffusion-convection problem. We assume that the growth coefficient of the convection term lies in the Marcinkiewicz spaceweak-LN.
Nonlinearity, 1993
The author establishes Poincare and Sobolev type inequalities involving powers of the Jacobian de... more The author establishes Poincare and Sobolev type inequalities involving powers of the Jacobian determinant of a quasiregular mapping as a weight.
Nonlinear Analysis: Theory, Methods & Applications, 1984
Journal of Fixed Point Theory and Applications, 2007
. Let $$a_j : {\mathbb{R}} \rightarrow {\mathbb{R}}$$ be a sequence of Borel measurable function... more . Let $$a_j : {\mathbb{R}} \rightarrow {\mathbb{R}}$$ be a sequence of Borel measurable functions satisfying, for a function $$K \in L_{\rm loc}^{1}, K : {\mathbb{R}} \rightarrow [1,\infty),$$ the inequalities $$ 1/K(x) \leq a_j (x) \leq K(x)\quad {\rm a.e.}\, x \in {\mathbb{R}} $$ and suppose $$ a_j \rightharpoonup a\quad {\rm in}\,\sigma(L^1, L^\infty). $$ Then there exists a sequence of increasing homeomorphisms $$h_j
Functiones et Approximatio Commentarii Mathematici, 2009
We show that, for Ω a bounded convex domain of R 2 , any 2 × 2 symmetric matrix A(x) with det A(x... more We show that, for Ω a bounded convex domain of R 2 , any 2 × 2 symmetric matrix A(x) with det A(x) = 1 for a.e. x ∈ Ω satisfying the ellipticity bounds |ξ| 2 H A(x)ξ, ξ H|ξ| 2 for a.e. x ∈ Ω and for all ξ ∈ R 2 can be approximated, in the sense of G-convergence, by a sequence of matrices of the type γ j (x) 0 0 1 γ j (x) with H − H 2 − 1 γ j (x) H + H 2 − 1 .
Communications on Pure and Applied Analysis, 2010
ABSTRACT We study planar homeomorphisms f:Ω⊂ℝ 2 @&gt;onto&gt;&gt;Ω &#39; ⊂ℝ 2 , f... more ABSTRACT We study planar homeomorphisms f:Ω⊂ℝ 2 @&gt;onto&gt;&gt;Ω &#39; ⊂ℝ 2 , f=(u,v), which are Absolutely Continuous on Lines parallel to the axes (ACL) together with their inverse f -1 . The main result is that u and v have almost everywhere the same critical points. This generalizes a previous result [S. Hencl, G. Moscariello, A. Passarelli di Napoli and S. Sbordone, J. Math. Anal. Appl. 355, No. 1, 22–32 (2009; Zbl 1169.30007)] concerning bi-Sobolev mappings. Moreover we construct an example of a planar ACL-homeomorphism not belonging to the Sobolev class W loc 1,1 .
Calculus of Variations and Partial Differential Equations, 2008
We show that the limit f of a weakly convergent sequence of W 1,1 homeomorphisms f j with finite ... more We show that the limit f of a weakly convergent sequence of W 1,1 homeomorphisms f j with finite distortion has finite distortion as well, provided that it is a homeomorphism. Moreover, the lower semicontinuity of the distortions is deduced both in case of outer and inner distortion.
Calculus of Variations and Partial Differential Equations, 2013
ABSTRACT We establish a quantitative version of distortion inequality for mappings of bounded inn... more ABSTRACT We establish a quantitative version of distortion inequality for mappings of bounded inner distortion. Some applications to the integral form of the isoperimetric inequality are given.
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Papers by Gioconda Moscariello