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Selected problems on elliptic equations involving measures
elliptic equations involving measures Analysis of PDEs
2012/4/18
This monograph concerns linear and nonlinear Dirichlet problems involving L^1 data and more generally measure data, based on Stampacchia's definition of weak solution. We explain some of the main tool...
From $L$-series of elliptic curves to Mahler measures
Mahler measure L-value of elliptic curve hypergeometric series
2011/1/21
We prove the conjectural relations between Mahler measures and L-values of elliptic curves of conductors 20 and 24. We also present new hyper-geometric expressions for L-values of CM elliptic curves o...
Fractal curvature measures and Minkowski content for one-dimensional self-conformal sets
Fractal curvature measures Minkowski one-dimensional self-conformal sets
2011/2/28
We investigate intrinsic geometric properties of invariant sets of one-dimensional conformal iterated function systems. We show that for such a set F the fractal cur-vature measures exist, if and only...
On the abundance of non-zero central Lyapunov exponents, physical measures and stable ergodicity for partially hyperbolic dynamics
u-Gibbs states physical measures partially hyperbolic dynamics minimal foliations
2011/1/20
We show that each strongly partially hyperbolic C2 diffeomorphism, with one-dimensional subbundles and C2 smooth andminimal strong-unstable foliation, is C2 close to a diffeomorphism having non-zero c...