Related papers: Martingale problems for some degenerate Kolmogorov…
We prove Kolmogorov's law of the iterated logarithm for noncommutative martingales. The commutative case was due to Stout. The key ingredient is an exponential inequality proved recently by Junge and the author.
In this manuscript, we provide local $L^q$-estimates for the gradient of solutions of a class of quasilinear equations whose principal part lacks strong monotonicity. These estimates are used to establish uniform large-scale $L^q$-estimates…
We consider a class of ultra-parabolic Kolmogorov-type operators satisfying the Hormander's condition. We prove an intrinsic Taylor formula with global and local bounds for the remainder given in terms of the norm in the homogeneous Lie…
We review recent progress in the fractional Calder\'on problem, where one tries to determine an unknown coefficient in a fractional Schr\"odinger equation from exterior measurements of solutions. This equation enjoys remarkable uniqueness…
The aim of this work is to prove the existence of a fundamental solution associated to the Kolmogorov equation L u = f with measurable coefficients in the dilation invariant case. Moreover, we prove Gaussian upper and lower bounds for it,…
We study the degenerate Kolmogorov equations (also known as kinetic Fokker-Planck equations) in nondivergence form. The leading coefficients $a^{ij}$ are merely measurable in $t$ and satisfy the vanishing mean oscillation (VMO) condition in…
We introduce and study some backward Kolmogorov equations associated to stochastic filtering problems. Measure-valued processed arise naturally in the context of stochastic filtering and one can formulate two stochastic differential…
We obtain new local Calderon-Zygmund estimates for elliptic equations with matrix-valued weights for linear as well as non-linear equations. We introduce a novel log-BMO condition on the weight M. In particular, we assume smallness of the…
Extended systems governed by partial differential equations can, under suitable conditions, be approximated by means of sets of ordinary differential equations for global quantities capturing the essential features of the systems dynamics.…
In this article we consider the simultaneous recovery of bulk and boundary potentials in (degenerate) elliptic equations modelling (degenerate) conducting media with inaccessible boundaries. This connects local and nonlocal Calder\'on type…
In recent developments, a general approach for solving Riemann--Hilbert problems numerically has been developed. We review this numerical framework, and apply it to the calculation of orthogonal polynomials on the real line. Combining this…
Pointwise estimates for the gradient of solutions to the $p$-Laplace system with right-hand side in divergence form are established. They enable us to develop a nonlinear counterpart of the classical Calder\'on-Zygmund theory in terms of…
We establish new intrinsic Strichartz estimates for solutions of the Cauchy problem for a class of possibly degenerate Schr\"odinger equations with a real drift.
We establish several fine boundary regularity results of weak solutions to non-homogeneous $s$-fractional Laplacian type equations. In particular, we prove sharp Calder\'on-Zygmund type estimates of $u/d^s$ depending on the regularity…
We present existence results for weak solutions to a broad class of degenerate McKean-Vlasov equations with rough coefficients, expanding upon and refining the techniques recently introduced by the third author. Under certain structural…
In this paper, we investigate Kolmogorov type theorems for small perturbations of degenerate Hamiltonian systems. These systems are index by a parameter $\xi$ as \( H(y,x,\xi) = \langle\omega(\xi),y\rangle + \varepsilon…
We prove fine higher regularity results of Calder\'on-Zygmund-type for equations involving nonlocal operators modelled on the fractional $p$-Laplacian with possibly discontinuous coefficients of VMO-type. We accomplish this by establishing…
In this paper matrix orthogonal polynomials in the real line are described in terms of a Riemann--Hilbert problem. This approach provides an easy derivation of discrete equations for the corresponding matrix recursion coefficients. The…
We consider Fokker--Planck--Kolmogorov equations with unbounded coefficients and obtain upper estimates of solutions. We also obtain new estimates involving Lyapunov functions.
Inspired by an article of Cotti, Dubrovin and Guzzetti arXiv:1706.04808, we extend to a degenerate case a result of Malgrange on integrable deformations of irregular singularities. We give an application to integrable deformations of the…