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G Velo - One of the best experts on this subject based on the ideXlab platform.
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generalized strichartz inequalities for the wave equation
Journal of Functional Analysis, 1995Co-Authors: J Ginibre, G VeloAbstract:Abstract We make a synthetic exposition of the generalized Strichartz inequalities for the wave equation obtained in [6] together with the limiting cases recently obtained in [13] with as simple proofs as possible. The proofs combine stationary phase estimates, dyadic decompositions, the Hardy-Littlewood Inequality or the Holder Inequality in time, and abstract duality and interpolation arguments.
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regular articlegeneralized strichartz inequalities for the wave equation
Journal of Functional Analysis, 1995Co-Authors: J Ginibre, G VeloAbstract:We make a synthetic exposition of the generalized Strichartz inequalities for the wave equation obtained in [6] together with the limiting cases recently obtained in [13] with as simple proofs as possible. The proofs combine stationary phase estimates, dyadic decompositions, the Hardy-Littlewood Inequality or the Holder Inequality in time, and abstract duality and interpolation arguments.
J Ginibre - One of the best experts on this subject based on the ideXlab platform.
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generalized strichartz inequalities for the wave equation
Journal of Functional Analysis, 1995Co-Authors: J Ginibre, G VeloAbstract:Abstract We make a synthetic exposition of the generalized Strichartz inequalities for the wave equation obtained in [6] together with the limiting cases recently obtained in [13] with as simple proofs as possible. The proofs combine stationary phase estimates, dyadic decompositions, the Hardy-Littlewood Inequality or the Holder Inequality in time, and abstract duality and interpolation arguments.
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regular articlegeneralized strichartz inequalities for the wave equation
Journal of Functional Analysis, 1995Co-Authors: J Ginibre, G VeloAbstract:We make a synthetic exposition of the generalized Strichartz inequalities for the wave equation obtained in [6] together with the limiting cases recently obtained in [13] with as simple proofs as possible. The proofs combine stationary phase estimates, dyadic decompositions, the Hardy-Littlewood Inequality or the Holder Inequality in time, and abstract duality and interpolation arguments.
Steve Hofmann - One of the best experts on this subject based on the ideXlab platform.
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a weak reverse Holder Inequality for caloric measure
Journal of Geometric Analysis, 2020Co-Authors: Alyssa Genschaw, Steve HofmannAbstract:Following a result of Bennewitz–Lewis for non-doubling harmonic measure, we prove a criterion for non-doubling caloric measure to satisfy a weak reverse Holder Inequality on an open set $$\Omega \subset \mathbb {R}^{n+1}$$, assuming as a background hypothesis only that the essential boundary of $$\Omega $$ satisfies an appropriate parabolic version of Ahlfors–David regularity (which entails some backwards in time thickness). We also show that the weak reverse Holder estimate is equivalent to solvability of the initial Dirichlet problem with “lateral” data in $$L^p$$, for some $$p<\infty $$, in this setting.
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a weak reverse Holder Inequality for caloric measure
arXiv: Analysis of PDEs, 2018Co-Authors: Alyssa Genschaw, Steve HofmannAbstract:Following a result of Bennewitz-Lewis for non-doubling harmonic measure, we prove a criterion for non-doubling caloric measure to satisfy a weak reverse Holder Inequality on an open set $\Omega$, assuming as a background hypothesis only that the essential boundary of $\Omega$ satisfies an appropriate parabolic version of Ahlfors-David regularity (which entails some backwards in time thickness). We also show that the weak reverse Holder estimate is equivalent to solvability of the initial Dirichlet problem with "lateral" data in $L^p$, for some $p<\infty$, in this setting.
Genschaw Alyssa - One of the best experts on this subject based on the ideXlab platform.
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A Weak Reverse Holder Inequality for Caloric Measure
2019Co-Authors: Genschaw Alyssa, Hofmann SteveAbstract:Following a result of Bennewitz-Lewis for non-doubling harmonic measure, we prove a criterion for non-doubling caloric measure to satisfy a weak reverse Holder Inequality on an open set $\Omega$, assuming as a background hypothesis only that the essential boundary of $\Omega$ satisfies an appropriate parabolic version of Ahlfors-David regularity (which entails some backwards in time thickness). We also show that the weak reverse Holder estimate is equivalent to solvability of the initial Dirichlet problem with "lateral" data in $L^p$, for some $p
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Absolute continuity of parabolic measure and the initial-dirichlet problem
University of Missouri--Columbia, 2019Co-Authors: Genschaw AlyssaAbstract:This thesis is devoted to the study of parabolic measure corresponding to a divergence form parabolic operator. We first extend to the parabolic setting a number of basic results that are well known in the elliptic case. Then following a result of Bennewitz-Lewis for non-doubling harmonic measure, we prove a criterion for non-doubling caloric measure to satisfy a weak reverse Holder Inequality on an open set [omega] R(n+1), assuming as a background hypothesis only that the essential boundary of [omega] satisfies an appropriate parabolic version of Ahlfors-David regularity (which entails some backwards in time thickness). We then show that the weak reverse Holder estimate is equivalent to solvability of the initial Dirichlet problem with "lateral" data in [Lp], for some p< [infinity]. Finally, we prove that for the heat equation, BMO-solvability implies scale invariant quantitative absolute continuity of caloric measure with respect to surface measure, in an open set [omega] with time-backwards ADR boundary. Moreover, the same results apply to the parabolic measure associated to a uniformly parabolic divergence form operator (L), with estimates depending only on dimension, the ADR constants, and parabolicity, provided that the continuous Dirichlet problem is solvable for (L) in [omega]. By a result of Fabes, Garofalo and Lanconelli [FGL], this includes the case of [C1]-Dini coefficients.Includes bibliographical reference
Alyssa Genschaw - One of the best experts on this subject based on the ideXlab platform.
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a weak reverse Holder Inequality for caloric measure
Journal of Geometric Analysis, 2020Co-Authors: Alyssa Genschaw, Steve HofmannAbstract:Following a result of Bennewitz–Lewis for non-doubling harmonic measure, we prove a criterion for non-doubling caloric measure to satisfy a weak reverse Holder Inequality on an open set $$\Omega \subset \mathbb {R}^{n+1}$$, assuming as a background hypothesis only that the essential boundary of $$\Omega $$ satisfies an appropriate parabolic version of Ahlfors–David regularity (which entails some backwards in time thickness). We also show that the weak reverse Holder estimate is equivalent to solvability of the initial Dirichlet problem with “lateral” data in $$L^p$$, for some $$p<\infty $$, in this setting.
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a weak reverse Holder Inequality for caloric measure
arXiv: Analysis of PDEs, 2018Co-Authors: Alyssa Genschaw, Steve HofmannAbstract:Following a result of Bennewitz-Lewis for non-doubling harmonic measure, we prove a criterion for non-doubling caloric measure to satisfy a weak reverse Holder Inequality on an open set $\Omega$, assuming as a background hypothesis only that the essential boundary of $\Omega$ satisfies an appropriate parabolic version of Ahlfors-David regularity (which entails some backwards in time thickness). We also show that the weak reverse Holder estimate is equivalent to solvability of the initial Dirichlet problem with "lateral" data in $L^p$, for some $p<\infty$, in this setting.