TITLE

# Partial regularity for non autonomous functionals with non standard growth conditions

AUTHOR(S)
De Maria, Bruno; Passarelli di Napoli, Antonia
PUB. DATE
July 2010
SOURCE
Calculus of Variations & Partial Differential Equations;Jul2010, Vol. 38 Issue 3/4, p417
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
We prove a C1, Î¼ partial regularity result for minimizers of a non autonomous integral funcitional of the form under the so-called non standard growth conditions. More precisely we assume that for 2 â‰¤ p < q and that D z f( x, z) is Î±-HÃ¶lder continuous with respect to the x-variable. The regularity is obtained imposing that $${\frac{p}{q} < \frac{n+\alpha}{n}}$$ but without any assumption on the growth of $${D^{2}_{z}f}$$.
ACCESSION #
50354933

## Related Articles

• Recovering unknown terms in a nonlinear boundary condition for Laplace's equation. Fasino, Dario; Inglese, Gabriele // IMA Journal of Applied Mathematics;Dec2006, Vol. 71 Issue 6, p832

We consider a thin metallic plate whose top side is inaccessible and in contact with a corroding fluid. Heat exchange between metal and fluid follows linear Newton's cooling law as long as the inaccessible side is not damaged. We assume that the effects of corrosion are modelled by means of a...

• Integrable lattices and their sublattices: From the discrete Moutard (discrete Cauchy-Riemann) 4-point equation to the self-adjoint 5-point scheme. Doliwa, A.; Grinevich, P.; Nieszporski, M.; Santini, P. M. // Journal of Mathematical Physics;Jan2007, Vol. 48 Issue 1, p013513

We present the sublattice approach, a procedure to generate, from a given integrable lattice, a sublattice which inherits its integrability features. We consider, as illustrative example of this approach, the discrete Moutard 4-point equation and its sublattice, the self-adjoint 5-point scheme...

• Explicit solutions of boundary-value problems for (2 + 1)-dimensional integrable systems. Vereshchagin, V. // Mathematical Notes;Mar2013, Vol. 93 Issue 3/4, p360

Two nonlinear integrable models with two space variables and one time variable, the Kadomtsev-Petviashvili equation and the two-dimensional Toda chain, are studied as well-posed boundary-value problems that can be solved by the inverse scattering method. It is shown that there exists a multitude...

• Asymptotic Properties of Harmonic and M-Harmonic Functions near the Boundary of the Unit Ball. Roginskaya, M. M. // Journal of Mathematical Sciences;May2003, Vol. 115 Issue 2, p2262

It is shown that decompositions of a plurisubharmonic measure on a sphere of $\Bbb C^n$ with respect to the Hausdorff dimension scales related to the Euclidean and KorÃ¡nyi metrics coincide under a linear correspondence of indices. Bibliography: 7 titles.

• Multivalent Harmonic Uniformly Starlike Functions. Ahuja, Om; Joshi, Santosh; Sangle, Naveneet // Kyungpook Mathematical Journal;Sep2009, Vol. 49 Issue 3, p545

In this paper, we investigate a generalized family of complex-valued harmonic functions that are multivalent, sense-preserving, and are associated with k-uniformly harmonic functions in the unit disk. The results obtained here include a number of known and new results as their special cases.

• Solvability of boundary value problems with the nonlocal Bitsadze-Samarskii condition for linear hyperbolic equations. Kozhanov, A. I. // Doklady Mathematics;Jun2010, Vol. 81 Issue 3, p467

The article provides information on the applicability of the nonlocal Bitsadze-Samarskii condition equation in solving the linear hyperbolic equations' boundary value problems. It presents the several boundary value problems along with their respective formula as well as the solution. It...

• Recent Developments on Hybrid Time-Frequency Numerical Simulation Techniques for RF and Microwave Applications. Oliveira, Jorge F.; Pedro, José C. // Journal of Function Spaces & Applications;2013, p1

This paper reviews some of the promising doors that functional analysis techniques have recently opened in the field of electronic circuit simulation. Because of the modulated nature of radio frequency (RF) signals, the corresponding electronic circuits seem to operate in a slow time scale for...

• ELLIPTIC REGULARITY AND SOLVABILITY FOR PARTIAL DIFFERENTIAL EQUATIONS WITH COLOMBEAU COEFFICIENTS. Hörmann, Günther; Oberguggenberger, Michael // Electronic Journal of Differential Equations;2004, Vol. 2004, p1

This paper addresses questions of existence and regularity of solutions to linear partial differential equations whose coefficients are generalized functions or generalized constants in the sense of Colombeau. We introduce various new notions of ellipticity and hypoellipticity, study their...

• Local a posteriori estimates for the Stokes problem. Repin, S. I. // Journal of Mathematical Sciences;Jul2006, Vol. 136 Issue 2, p3786

We obtain computable estimates of the difference between an exact solution of the Stokes problem and an approximation from a respective energy class. The estimates are presented in terms of local norms and linear functionals. Certain generalizations to some nonlinear problems are discussed....

Share