Lewy-Stampacchia type estimates for variational inequalities driven by (non)local operators

By Raffaella Servadei, Enrico Valdinoci. 2013

208 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/a38e4bf5f592ad82d7dd2c7de5747f5d19a2e83e

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

On a fractional degenerate Kirchhoff-type problem (2017, background): “The reader interested in knowing more about fractional Sobolev spaces is invited to consult the very nice survey paper [19] and the references therein, while for more details on X and X0 we refer to the papers [38, 39, 40, 41, 42], where these functional spaces were introduced and analysed in their ”
Three Weak Solutions for Nonlocal Fractional Equations (2014, unknown): “For further details on the fractional Sobolev spaces we refer to [1] and to the references therein, while for other details on X and X0 we refer to [12], where these functional spaces were introduced, and also to [11, 13, 14, 15], where various properties of these spaces were proved.”
Existence of solutions for Kirchhoff type problem involving the non-local fractional p-Laplacian (2015, methodology): “It is worth mentioning that our functional setting above is inspired by the pioneering works of Servadei and Valdinoci in [38,39], in which the corresponding functional framework was discussed as p = 2.”
Lower semicontinuity of functionals of fractional type and applications to nonlocal equations with critical Sobolev exponent (2015, methodology): “The space X0 was introduced in [32] in a general nonlocal framework, in order to give a variational formulation for nonlocal integrodifferential equations of fractional type depending on a suitable kernel K.”
Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: A unified approach via fractional De Giorgi classes (2016, background): “In the quadratic case p = 2, spaces of this kind have been for instance considered in [57, 58].”
Existence results for fractional p-Laplacian problems via Morse theory (2014, methodology): “Several existence results via variational methods are proved in a series of papers of Servadei & Valdinoci [40–43] (see also Iannizzotto & Squassina [20] for the special case s = 1/2, p = 2 and N = 1, with exponential nonlinearity).”
The abstract Lewy-Stampacchia inequality and applications (2014, methodology): “A similar procedure can be exploited to deal with non-homogeneous boundary conditions, see [30] for some examples of this transition from an abstract result to concrete applications.”
Multiplicity results for elliptic fractional equations with subcritical term (2015, background): “Notations and definitions In this subsection we briefly recall some properties of the functional space X0, firstly introduced in [21], and we give some notations.”
Existence of three solutions for Kirchhoff nonlocal operators of elliptic type (2013, methodology): “We know that X and X0 are nonempty, since C 2 0 (Ω) ⊆ X0 by Lemma 11 of [14].”
A critical fractional equation with concave-convex power nonlinearities (2013, methodology): “We ﬁx k 0 ∈ I , and we consider .61) Taking the derivative of the identity given in (1.6), see also [39, Lemma 16], for any u,ϕ ∈ X s 0 (Ω) we obtain that .62) Then, using φ ε (z m ) + as a test function in (2.55), by (2.62), and the fact that (cid”