Elliptic complexes in the calculus of variations
Alcuni problemi relativi ai complessi ellittici
Variational integrals for elliptic complexes
We discuss variational integrals which are defined on differential forms associated with a given first order elliptic complex. This general framework provides us with better understanding of the concepts of convexity, even in the classical setting
Lower semicontinuity of a class of multiple integrals below the growth exponent
On the continuity of degenerate n-harmonic functions
We study the regularity of finite energy solutions to degenerate
On weak Hessian determinants
We consider and study several weak formulations of the Hessian determinant, arising by formal integration by parts. Our main concern are their continuity properties. We also compare them with the Hessian measure.
On the continuity of degenerate -harmonic functions
We study the regularity of finite energy solutions to degenerate -harmonic equations. The function (), which measures the degeneracy, is assumed to be subexponentially integrable, it verifies the condition exp(()) ∈ . The function () is increasing on [0,∞[ and satisfies the divergence condition
Divergence forms of the infinity-Laplacian.
The central theme running through our investigation is the infinity-Laplacian operator in the plane. Upon multiplication by a suitable function we express it in divergence form, this allows us to speak of weak infinity-harmonic function in W1,2. To every infinity-harmonic function u we associate its conjugate function v. We focus our attention to the first order Beltrami type equation for h= u + iv
Regularity results for vector fields of bounded distortion and applications.
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