Multiple Integrals In The Calculus Of Variations And Nonlinear Elliptic Systems

By G. Eisenhauer. 2016

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Citations in the corpus

Quantitative stochastic homogenization of convex integral functionals (2014, background): “found in Giaquinta [10], and a scaling argument.”
On the local regularity of suitable weak solutions to the generalized Navier–Stokes equations (2014, unknown): “[8] ) we get ‖u‖2 L3(t0−R2;L18/5(BR)) + ‖∇u‖ 2 L(2)(QR) ≤ cR−1 ( ‖u‖2 L3(t0−4R2;L9/4(B2R)) + ‖u‖ 3 L(3)(Q2R) ) .”
On C1, C2, and weak type-(1,1) estimates for linear elliptic operators (2016, methodology): “10 are based on Campanato’s approach, which was used previously, for instance, in [10, 13].”
Growth conditions and regularity for weak solutions to nonlinear elliptic pdes (2020, methodology): “[46] M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Annals of Mathematics Studies, vol. 105, Princeton University Press, Princeton, NJ, 1983.”
Partial Regularity for BV Minimizers (2018, methodology): “Hereby he proved partial regularity of minimizers under controlled quadratic growth conditions (see [45] and [40] for the terminology).”
Gradient estimates for solutions of the Lam\'e system with partially infinite coefficients in dimensions greater than two (2016, unknown): “5 in [23]) and the Sobolev embedding theorem, we have, for some p > 3, ‖∇W‖L∞(Q1/2) ≤ C ‖W‖W2,p(Q1/2) ≤ C ( ‖∇W‖L2(Q1) + ∥∥Lλ,μU ∥∥ L∞(Q1) ) ,”
Lipschitz estimates for systems with ellipticity conditions at infinity (2016, methodology): “Then, further regularity follows from the regularity theory for linear elliptic systems with smooth coefficients (see for instance Section 3 of [19]).”
Recent developments in problems with nonstandard growth and nonuniform ellipticity (2021, background): “1), is very much a classical topic, for which we refer to the treatises [118,120,122,148,177] and to the more recent survey [173].”
Liouville type theorem for stationary Navier–Stokes equations (2015, background): “It is known, see for instance [4] (this is just a matter of suitable iterations), that such an inequality implies the following Caccioppoli type inequality”
Higher Differentiability of Solutions of Elliptic Systems with Sobolev Coefficients: The Case p = n = 2 (2014, background): “3) For an exhaustive treatment of the regularity of solutions of elliptic systems under the assumptions (H0)– (H2) and (H3′), or local minimizers under the assumptions (F1)–(F4) and (F5′), we refer the interested reader to [17, 18] and the references therein.”