Gradient estimates for the p (x)-Laplacean system

By E. Acerbi, Giuseppe Mingione. 2005

474 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/dac741aee4dc12e7853512a67eb385f5b819f148

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Regularity of minima: An invitation to the dark side of the calculus of variations (2006, methodology): “maximal type operator, we cannot use the so called “good-λ-inequality” principle as in [8]; on the contrary, we introduce an analog version of that, working again on Calderón-Zygmund cubes directly: we called it the “large-M -inequality” principle.”
Nonlinear Measure Data Problems (2011, methodology): “1) whenever x, y ∈ R and α ∈ [0, 1].”
Overview of differential equations with non-standard growth (2010, background): “[27] Acerbi, E.; Mingione, G.: Regularity results for a class of quasiconvex functionals with nonstandard growth.”
Entropy solutions for the p(x)-Laplace equation (2009, result): “Recently, Acerbi and Mingione [2] derived Calderón–Zygmung type estimates for (1), extending previous results of DiBenedetto and Manfredi [11] for the model problem (7) and p(·) ≡ p constant.”
Regularity of solutions to a class of variable–exponent fully nonlinear elliptic equations (2018, result): “In line with this observation, the results in [5] intersect those two approaches.”
Higher integrability for parabolic systems with non-standard growth and degenerate diffusions (2011, methodology): “Finally, a complete Calderón-Zygmund theory for equations with non-standard p(x)-growth was achieved by Acerbi and Mingione [3].”
Calderón–Zygmund estimates for parabolic p(x,t)-Laplacian systems (2014, methodology): “Later, extensions to general parabolic systems were obtained by Duzaar, Mingione, and Steffen [22] while a Calderón–Zygmund theory for evolutionary obstacle problems can be found in [12], [33].”
Gradient estimates for a class of parabolic systems (2007, methodology): “We observe interesting similarities with the estimates obtained in the elliptic case (3) via maximal function techniques in [1], [10], and [14]; this is not surprising since the local use of estimates (18) and (21), in combination with Vitali’s covering lemma, in some sense emulates the use of the m”
The Singular Set of Minima of Integral Functionals (2006, methodology): “As for the nonhomogeneous right-hand side, this plays the same role as the map g, see [ 2 ] for the treatment of such a term.”
Fractional double-phase patterns: concentration and multiplicity of solutions (2020, methodology): “We refer to Acerbi and Mingione [1] in the context of gradient estimates and contributions to the qualitative analysis of minimizers of nonstandard energy functionals with variable coefficients.”