Regularity for minimizers for functionals of double phase with variable exponents

By M. Alessandra Ragusa, A. Tachikawa. Advances in Nonlinear Analysis, 2019

332 citations recorded by the source corpus.

Abstract The functionals of double phase type H(u):=∫|Du|p+a(x)|Du|qdx, (q>p>1, a(x)≥0) $$\begin{array}{} \displaystyle {\cal H} (u):= \int \left(|Du|^{p} + a(x)|Du|^{q} \right) dx, ~~ ~~~(q \gt p \gt 1,~~a(x)\geq 0) \end{array}$$ are introduced in the epoch-making paper by Colombo-Mingione [1] for constants p and q, and investigated by them and Baroni. They obtained sharp regularity results for minimizers of such functionals. In this paper we treat the case that the exponents are functions of x and partly generalize their regularity results.

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

View Paper: https://www.semanticscholar.org/paper/e7a78d059e7c6a9d77396c1ad18a242cf01ac4ca

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Citations in the corpus

Existence of solutions for singular double phase problems via the Nehari manifold method (2021, unknown): “We mention the papers of Baroni–Colombo–Mingione [4–6], Baroni–Kuusi–Mingione [7], Byun– Oh [9, 10], Byun–Youn [11], Colombo–Mingione [14–16], De Filippis–Mingione [18–20], De Filippis–Palatucci [21], Esposito–Leonetti–Mingione [23], Esposito– Leonetti–Petricca [24],Marcellini [37–39], Ok [44, 45], ”
Growth conditions and regularity for weak solutions to nonlinear elliptic pdes (2020, unknown): “For related recent references we also quote Duzgun-Marcellini-Vespri [39], [40], Rǎdulescu-Zhang [63], [64], Cencelja-Rădulescu-Repovš [19], Papageorgiou-Rădulescu-Repovš-Dušan [62], Ambrosio-Rădulescu [1], Ragusa-Tachikawa [65], Chlebicka [20], Chlebicka-DeFilippis [21], [22], CupiniGiannetti-Giova”
New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems (2022, methodology): “In this direction we mention the works of Baroni-ColomboMingione [5, 6, 7], Baroni-Kuusi-Mingione [8], Byun-Oh [12], Colombo-Mingione [17, 18], De Filippis [19], De Filippis-Palatucci [26], Harjulehto-Hästö-Toivanen [38], Marcellini [51, 52], Ok [58, 59], Ragusa-Tachikawa [62, 63] and the references”
Existence Results for Double Phase Problem in Sobolev–Orlicz Spaces with Variable Exponents in Complete Manifold (2021, background): “For more details, we refer the reader to [3, 10, 13, 16, 15, 21, 18, 23] and the references therein.”
An existence result for singular Finsler double phase problems (2020, methodology): “We mention the papers of BaroniColombo-Mingione [3–5], Baroni-Kuusi-Mingione [6], Colombo-Mingione [12,13], Marcellini [32,31], Ok [35,36], Ragusa-Tachikawa [42] and the references therein.”
Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold (2020, unknown): “We refer to the works of Baroni-Colombo-Mingione [4], [5], [6], Baroni-Kuusi-Mingione [7], CupiniMarcellini-Mascolo [16], Colombo-Mingione [14], [15], Marcellini [27], [28], Ok [33], [34], Ragusa-Tachikawa [43] and the references therein.”
Maximal regularity for local minimizers of non-autonomous functionals (2019, background): “ψ(t)+a(x)ξ(t), e.g. [17]. VIII. Triple phase: tp+a(x)tq+ b(x)tr, e.g. [30, 43]. IX. Double variable exponent: tp(x) +tq(x), e.g. [22, 76, 84]. X. Variable exponent double phase tp(x) +a(x)tq(x), e.g. [62, 77]. In this paper, we establish a general regularity theory for non-autonomous functionals wit”