Gradient potential estimates

By Giuseppe Mingione. 2011

250 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9388ad92fa6ee95480e3f6f6c498a1e7c82f3e4f

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Gradient estimates via non-linear potentials (2009, background): “tively. The estimates in (6.13) refer to Rn+1 as supporting domain, but they can be localized using cut-oﬀ functions and therefore yield local estimates for caloric Riesz potentials; see for instance [48, 49]. The ﬁnal outcome is the following result: Theorem 6.1. Let u ∈ L 1(−T,0;W1, (Ω)) be a SOLA”
The obstacle problem for nonlinear integro-differential operators (2016, background): “For other fractional Caccioppoli-type inequalities, though not taking into account the tail contribution, see [17,31,32].”
Existence results for fractional p-Laplacian problems via Morse theory (2014, methodology): “A fractional version of De Giorgi’s iteration method was developed by Mingione [31].”
Nonlinear Measure Data Problems (2011, methodology): “In [79] a precise local analog of the second estimate in (2.”
Local Lipschitz regularity for degenerate elliptic systems (2009, background): “e is the so called Wolﬀ potential deﬁned by WV β,p(x,R) := ZR 0 |V|(B(x,)) n−βp 1 p−1 d β<n/p, where V is a Radon measure. In this respect pointwise estimates for solutions are obtained in [22, 35, 30, 11]. The peculiarity of the non-linear potential introduced in (1.11) relies in that it allow”
Local behavior of fractional $p$-minimizers (2015, unknown): “Also, it is worth mentioning that other fractional Caccioppoli-type inequalities have been recently used in different contexts (see, for instance, [21, 22, 9]), although none of them takes into account the tails.”
Hitchhiker's guide to the fractional Sobolev spaces (2011, background): “equations, are now experiencing impressive applications in different subjects, such as, among others, the thin obstacle problem [87, 69], optimization [37], finance [26], phase transitions [2, 14, 88, 40, 45], stratified materials [83, 23, 24], anomalous diffusion [68, 98, 65], crystal dislocation [”
Riesz Potentials and Nonlinear Parabolic Equations (2013, background): “Very recently, in [25, 26, 37], it has been shown that, surprisingly enough, the regularity theory of possibly degenerate quasilinear elliptic equations of the type −div a(Du) = μ completely reduces to that of standard Poisson equation (1.”
Potential estimates and gradient boundedness for nonlinear parabolic systems (2012, background): “We refer to [32], [33] and [34] for a more detailed description of the setting and for further references.”
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].”
Riesz potential estimates for a general class of quasilinear equations (2015, background): “In the recent paper [26], see also [29, 36], Kuusi and Mingione proved a pointwise estimate for gradient of solutions to (1.”
Lorentz estimates for degenerate and singular evolutionary systems (2013, background): “…is that, sincew is solution to a systems with just time-dependent coefficients, Dw turns out to be locally bounded inQλ10rz̄(z̄), see [18, Chapter VIII], and moreover, since estimate (4.11) holds with a constant c depending on n,N, p, ν, L, we also have the explicit formula sup Qλ5rz̄ (z̄) |Dw|…”
Pointwise Calderón–Zygmund gradient estimates for the p -Laplace system (2015, unknown): “The study of pointwise elliptic gradient regularity has received an impulse from the papers [49] and [27], where Havin-Maz’ya-Wolff nonlinear potentials have been shown to yield precise estimates for the gradient of local solutions to nonlinear p-Laplacian type equations, but with right-hand side in”
Nonlocal Harnack inequalities (2014, background): “For other fractional Caccioppoli-type inequalities, see also [20, 21] and [9].”
Fractional p-eigenvalues (2013, unknown): “The interested reader is referred to [16, 17, 8].”