Name
Title | ||
|---|---|---|
A Potential Space Estimate for Solutions of Systems of Nonlocal Equations in Peridynamics. |
Abstract | ||
|---|---|---|
We show that weak solutions to the strongly coupled system of nonlocal equations of linearized peridynamics belong to a potential space with higher integrability. Specifically, we show that a function measuring local fractional derivatives of weak solutions to a linear system belongs to L-p for some p > 2 with no additional assumptions other than measurability and ellipticity of the coefficients. This is a nonlocal analogue of an inequality of Meyers for weak solutions to an elliptic system of equations. We also show that functions in L-p whose Marcinkiewicz-type integrals are in L-p in fact belong to the Bessel potential space L-s(p). Thus the fractional analogue of higher integrability of the solution's gradient is displayed explicitly. The distinction here is that the Marcinkiewicz-type integral exhibits the coupling from the nonlocal model and does not resemble other classes of potential-type integrals found in the literature. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1137/18M1189294 | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
Keywords | Field | DocType |
peridynamics,higher integrability,nonlocal coupled system,fractional Korn's inequality,potential spaces | Mathematical analysis,Potential space,Peridynamics,Mathematics | Journal |
Volume | Issue | ISSN |
51 | 1 | 0036-1410 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| James Scott | 1 | 3121 | 235.65 |
| Tadele Mengesha | 2 | 0 | 0.68 |