Universal potential estimates

By Tuomo Kuusi, Giuseppe Mingione. 2012

229 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e10e9a6fc606cd4666ae5e5f226cd7a0f81b7fa1

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Higher differentiability for solutions to a class of obstacle problems (2018, background): “the years, there have been intense research activities for the regularity of the obstacle problem in this direction (see in particular the fundamental techniques established in [32,33]).”
Gradient estimates for heat kernels and harmonic functions (2017, background): “In the classical setting, the fact that quantitative regularity for harmonic functions implies quantitative regularity for solutions to the Poisson equation is easy to prove and there is even an analog for certain non-linear equations, see [80].”
Fractional Differentiability for Solutions of Nonlinear Elliptic Equations (2016, background): “Under these assumptions many interesting bounds on the size and the oscillations of the solutions and gradients are established in [19] and [20].”
Regularity for quasilinear equations on degenerate singular sets (2012, background): “1) has become accessible just quite recently, through a rather sophisticated and powerful nonlinear potential theory, see [4, 7, 13, 14, 15].”
Nonlinear Measure Data Problems (2011, result): “In Section 7 we present a unified approach, introduced in [60], connecting pointwise nonlinear potential estimates and intermediate regularization properties of possibly degenerate elliptic equations.”
Lorentz estimates for degenerate and singular evolutionary systems (2013, background): “An analog of implications (2.2) and (2.3) would on the other hand hold for systems enjoying a peculiar structure, and this is called quasi-diagonal p-Laplacian (or Uhlenbeck) structure: a ( Du ) = g ( |Du|2 ) Du where g ( |Du|2 ) ≈ |Du|p−2.”
On a new class of fractional partial differential equations (2014, background): “We also mention the interesting work of Kuusi and Mingione [19], who use the fractional maximal function applied to the gradient as an heuristic for fractional differentiation in the development of regularity estimates for integer order nonlinear 3The authors would like to thank Moritz Kassmann for ”
Besov regularity for solutions of p-harmonic equations (2017, background): “A first nonlinear growth counterpart was found in [14] forA(x, ξ ) = ⟨A(x)ξ, ξ⟩ p−2 2 A(x)ξ , 2 ≤ p ≤ n, see also [17, 18].”
Pointwise Calderón–Zygmund gradient estimates for the p -Laplace system (2015, unknown): “Enhancements and extensions of these results, involving classical Riesz potentials instead of nonlinear potentials, are the object of a series of papers starting from [39, 38].”
Classification of positive D1,p(RN)-solutions to the critical p-Laplace equation in RN☆ (2015, background): “Therefore, for a, A fixed, it follows that wRn is uniformly bounded in L (BA \ Ba) and hence, by [9, 13, 14, 21, 23], it is also uniformly bounded in C(K), 0 < α < 1, for any compact set K ⊂ BA \ Ba.”
Radial symmetry and applications for a problem involving the $-\Delta_p(\cdot)$ operator and critical nonlinearity in~$\mathbb{R}^N$ (2014, background): “1, by standard C estimates (see [15, 26, 27, 43, 45]), we deduce that u is locally of class C.”