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    Item type:Item,
    On the Role of Riesz Potentials in Poisson\'s Equation and Sobolev Embeddings
    (2015)
    Garg, Rahul
    ;
    Spector, Daniel
    ;
    應用數學系
    ;
    Department of Applied Mathematics
    In this paper, we show how standard techniques can be used to obtain new "almost"-Lipschitz estimates for the classical Riesz potentials acting on L-P-spaces in the supercritical exponent. Whereas similar results are known to hold for Riesz potentials acting on L-P(Omega) for Omega subset of R-N a bounded domain (and also on Sobolev, Sobolev-Orlicz functions), our results concern the mapping properties of the Riesz potentials on all of R-N. Additionally, we introduce and prove sharp estimates on the modulus of continuity for a family of Riesz-type potentials. In particular, through a new representation via these Riesz-type potentials, we establish analagous results for the logarithmic potential. As applications of these continuity estimates, we deduce new regularity estimates for distributional solutions to Poisson\'s equation, as well as an alternative proof of the supercritical Sobolev embedding theorem first shown by Brezis and Wainger in 1980.
  • Thumbnail Image
    Item type:Item,
    On the Role of Riesz Potentials in Poisson\'s Equation and Sobolev Embeddings
    (2015-01-01)
    Garg, Rahul
    ;
    Spector, Daniel
    ;
    應用數學系
    ;
    Department of Applied Mathematics
    In this paper, we show how standard techniques can be used to obtain new "almost"-Lipschitz estimates for the classical Riesz potentials acting on L-P-spaces in the supercritical exponent. Whereas similar results are known to hold for Riesz potentials acting on L-P(Omega) for Omega subset of R-N a bounded domain (and also on Sobolev, Sobolev-Orlicz functions), our results concern the mapping properties of the Riesz potentials on all of R-N. Additionally, we introduce and prove sharp estimates on the modulus of continuity for a family of Riesz-type potentials. In particular, through a new representation via these Riesz-type potentials, we establish analagous results for the logarithmic potential. As applications of these continuity estimates, we deduce new regularity estimates for distributional solutions to Poisson\'s equation, as well as an alternative proof of the supercritical Sobolev embedding theorem first shown by Brezis and Wainger in 1980.
  • Thumbnail Image
    Item type:Item,
    Design and Analysis of Ultra-Thin-Body SOI Based Subthreshold SRAM
    (2009)
    Hu, Vita Pi-Ho
    ;
    Wu, Yu-Sheng
    ;
    Fan, Ming-Long
    ;
    Su, Pin
    ;
    Chuang, Ching-Te
    This paper analyzes the stability, margin, and performance of Ultra-Thin-Body (UTB) SOI 6T/8T SRAM cells operating in subthreshold region. An analytical SNM model for UTB SOI 6T/8T SRAM cells operating in the subthreshold region is presented to investigate the Read SNM (RSNM) and Write SNM (WSNM). Our results indicate that back-gating technique is more effective in the subthreshold region than in the superthreshold region for improving RSNM and WSNM. The UTB SOI 6T SRAM cell with back-gating technique to increase the strength of the pull-up transistors and decrease the strength of the pass-gate transistors shows comparable RSNM in the subthreshold region with the 10T bulk subthreshold SRAM cell and an improvement in RSNM variation. Due to better electrostatic integrity, back-gating technique (pull-up PFET with positive back-gate bias, pull-down/pass-gate NFET's with negative back-gate bias) mitigates the 6T UTB SOI SRAM RSNM variation significantly with some improvement in RSNM. Increasing cell beta-ratio shows limited improvement on RSNM and has no benefit on SNM variability for subthreshold operation. The UTB SOI 8T SRAM cell exhibits RSNM 2X larger than the 6T SRAM cell in the subthreshold region. Mixed-mode device/circuit simulations show that 6T/8T UTB SOI SRAMs operating in the subthreshold region can meet/support the stability, leakage/density, and frequency requirements for intended application space of subthreshold SRAMs.