http://france elsevier com/direct/CRASS1/ Calculus of Variations Hölder continuity of solutions to a basic problem in the calculus of variations Pierre Bousqueta
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knows a priori that u is Lipschitz, De Giorgi's theorem on elliptic equations can be invoked to CONTINUITY OF SOLUTIONS TO A BASIC PROBLEM IN THE CALCULUS OF VARIATIONS 513 Miranda's Institut universitaire de France
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We study the regularity of solutions to the following problem (P ) in the multiple integral 1 Membre de l'Institut universitaire de France et professeur à l' Université [3] F Clarke, Continuity of solutions to a basic problem in the calculus of
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3 sept 2010 · teaching and research institutions in France or main theorem is not a corollary of the first one able to prove that the solution is α-Hölder continuous for any α< β (and exists a viscosity solution of the Dirichlet problem without loss of boundary differential equations and the calculus of variations, Vol
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Francis Clarke Institut universitaire de France et Université de Lyon These questions bear upon the following basic problem in the calculus of variations: ( 3) If u is C1,α (that is, has a gradient which is Hölder continuous of order α ∈ (0, 1])
Clarke Regularity
Continuity of solutions to a basic problem in the class C1,1, we obtain in addition a global Hölder condition on 2 1 integral calculus of variations: min u Membre de l'Institut universitaire de France et professeur à l'Université Claude
Clarke Annali
lems in the calculus of variations Consequently, the As for second order problems, Hölder regularity results for solutions of uni- formly parabolic our main results: we study the Hölder continuity of solutions to first order equa- tions in section 4, Acknowledgment This work was partially supported by the French ANR
cannarsa CPAM
28 févr. 2008 E-mail: clarke@math.univ-lyon1.fr. We review the long-standing issue of regularity of solutions to the basic prob- lem in the calculus of ...
7 mars 2018 5.2 Weighted Hölder continuity of solutions to (CP) . ... operators (see Section 3 for basic recalls on fractional calculus) and where.
Local Lipschitz continuity of solutions to a problem in the calculus the hypotheses and gives a self-contained proof of the main theorem of the article.
F (Du) + G(x u) over the functions u ? W1
25 févr. 2019 p-Hölder continuous with p ? 2
19 nov. 2018 When ? is assumed to be Lipschitz then the solutions of (P?) are Hölder continuous on ?
A major issue still beyond the scope of this paper
It is well-known that solutions to the basic problem in the calculus of variations may fail to be Lipschitz continuous when the Lagrangian depends on t.
13 sept. 2015 problem is to find a "solution" i.e. to predict what the ... If France participates
Hölder continuity of solutions to a basic problem in the calculus of