Guide to nonlinear potential estimates

T Kuusi, G Mingione - Bulletin of mathematical sciences, 2014 - Springer
One of the basic achievements in nonlinear potential theory is that the typical linear
pointwise estimates via fundamental solutions find a precise analog in the case of nonlinear …

Local Lipschitz continuity for p, q− PDEs with explicit u− dependence

P Marcellini - Nonlinear Analysis, 2023 - Elsevier
This article is dedicated to Emmanuele Di Benedetto, great mathematician, colleague,
friend. In the spirit to treat a subject that in the last years attracted the interest of several …

Vectorial nonlinear potential theory.

T Kuusi, G Mingione - Journal of the European Mathematical Society …, 2018 - ems.press
We settle the longstanding problem of establishing pointwise potential estimates for vectorial
solutions u:→ RN to the non-homogeneous p-Laplacean system− div (| Du| p− 2 Du)= µ in⊂ …

Linear potentials in nonlinear potential theory

T Kuusi, G Mingione - Archive for Rational Mechanics and Analysis, 2013 - Springer
Pointwise gradient bounds via Riesz potentials, such as those available for the linear
Poisson equation, actually hold for general quasilinear degenerate equations of p …

Universal potential estimates

T Kuusi, G Mingione - Journal of Functional Analysis, 2012 - Elsevier
We prove a class of endpoint pointwise estimates for solutions to quasilinear, possibly
degenerate elliptic equations in terms of linear and nonlinear potentials of Wolff type of the …

Nonlinear Calderón–Zygmund theory in the limiting case

B Avelin, T Kuusi, G Mingione - Archive for Rational Mechanics and …, 2018 - Springer
We prove a maximal differentiability and regularity result for solutions to nonlinear measure
data problems. Specifically, we deal with the limiting case of the classical theory of Calderón …

Riesz potential estimates for a general class of quasilinear equations

P Baroni - Calculus of Variations and Partial Differential …, 2015 - Springer
We consider solutions to nonlinear elliptic equations with measure data and general growth
and ellipticity conditions of degenerate type, as considered in Lieberman (Commun Partial …

[图书][B] Parabolic systems with polynomial growth and regularity

F Duzaar, G Mingione, K Steffen - 2011 - ams.org
We establish a series of optimal regularity results for solutions to general non-linear
parabolic systems\[u_t-\mathrm {div}\a (x, t, u, Du)+ H= 0\,,\] under the main assumption of …

The Wolff gradient bound for degenerate parabolic equations

T Kuusi, G Mingione - J. Eur. Math. Soc.(JEMS), 2014 - ems.press
The Wolff gradient bound for degenerate parabolic equations Page 1 DOI 10.4171/JEMS/449
J. Eur. Math. Soc. 16, 835–892 c European Mathematical Society 2014 Tuomo Kuusi …

Borderline global regularity for nonuniformly elliptic systems

C De Filippis, M Piccinini - International Mathematics Research …, 2023 - academic.oup.com
We establish sharp global regularity results for solutions to nonhomogeneous, nonuniformly
elliptic systems with zero boundary conditions imposed only on some part of the boundary of …